BEHAVIOR OF AUTOCLAVED AERATED CONCRETE SHEAR … thesis 2003-12-15.pdfUlises Max Cancino, M.S.E The...
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BEHAVIOR OF AUTOCLAVED AERATED CONCRETE SHEAR
WALLS WITH LOW-STRENGTH AAC
by
Ulises Max Cancino, B.S.E
Thesis
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
The University of Texas at Austin
December 2003
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BEHAVIOR OF AUTOCLAVED AERATED CONCRETE SHEAR
WALLS WITH LOW-STRENGTH AAC
Approved by Supervising Committee:
Richard E. Klingner, Supervisor
Oguzhan Bayrak
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Dedication
To my family.
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Acknowledgements
The experience of working at Ferguson Laboratory in the University of
Texas at Austin has been one of the most valuable experiences that I have had in
my life.
I would like to thank Dr. Richard Klingner for his tremendous support and
friendship during the entire process of the development of the project and after.
While I was under his supervision, I learned how to conduct a research project
professionally and also to understand the different theoretical aspects involved
during this study. Also, I would like to thank Dr. Oguzhan Bayrak for his support,
friendship and patience. As a result, I can evaluate this experience as an
invaluable opportunity to deepen my knowledge.
All of this research could have not been completed successfully without
the assistance of the staff at the Ferguson Structural Engineering Laboratory. I
give my recognition to the technicians: Blake Stasney, Mike Bell, Dennis Fillip
and Ray Madonna. Also, the assistance of the office staff has been really
important, and I offer my special thanks to Hortensia Peoples, Marie Jo Moore
and Regina Forward.
I would like to mention the undergraduates Geoff Mitchell and Ross
Sassen for their constant support of this project. My special recognition goes to
my friends Jorge Varela, Jaime Argudo and Jennifer Tanner, who continuously
supported me in different aspects of this research project and my progress. I
would also like to express my recognition to Gelberg Rodriguez, Ivan Ornelas,
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Leonardo Guim and Pedro Galvez. For them my best wishes on their own
success in their research projects.
Finally, and most importantly, I thank my mother, brother, cousin Hugo,
sister-in-law and my three nephews Natalia, Saschita and Anastasia and Karen
MacInnes, as they constantly encouraged me to finish this thesis successfully.
December 2003
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Abstract
Behavior of Autoclaved Aerated Concrete Shear Walls with Low-
Strength AAC
Ulises Max Cancino, M.S.E
The University of Texas at Austin, 2003
Supervisor: Richard E. Klingner
Three isolated full-scale shear walls of low-strength autoclaved aerated
concrete (AAC) were tested at the Structural Engineering Ferguson Laboratory of
the University of Texas at Austin. One specimen was constructed with vertical
panels, and the other two, with partially grouted reinforced masonry units. The
main objective of this study is to validate previously proposed design provisions
for low-strength AAC material. The variables considered in these shear wall
specimens were the compressive strength of the material, the flexural
reinforcement, and the geometry. Test results indicate good agreement between
observed and predicted behavior, and validate the previously proposed design
provisions. The results support the extension of those design provisions to low-
strength AAC shear-wall structures located in seismic zones.
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Table of Contents
CHAPTER 1 INTRODUCTION..................................................................................1
1.1 General .....................................................................................................1
1.2 Scope of Overall Study ..................................................................................1
1.3 Objectives of Overall Study ...........................................................................2
1.4 Organization of Overall Study .......................................................................2
1.5 Scope of Thesis ..............................................................................................3
1.6 Objectives of Thesis .......................................................................................4
1.7 Organization of this Thesis ............................................................................5
CHAPTER 2 TEST SPECIMENS, TEST SETUPS, AND TESTING PROCEDURES.........6
2.1 Introduction ....................................................................................................6
2.2 Design and Construction of Shear Wall Specimen 17 ...................................6 2.2.1 Objectives..............................................................................................6 2.2.2 Configuration of Shear Wall Specimen 17 ...........................................7 2.2.3 Test Setup for Shear Wall Specimen 17................................................9
2.2.3.1 Base Beam........................................................................9 2.2.3.2 Axial Load System .........................................................10 2.2.3.3 Lateral Bracing System ..................................................11 2.2.3.4 Actuators ........................................................................12 2.2.3.5 Instrumentation and Data Acquisition............................13
2.2.3.5.1 Instrumentation........................................................13 2.2.3.5.2 Data Acquisition......................................................17
2.2.4 Loading Protocol .................................................................................18
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2.2.5 Material Strengths ...............................................................................18 2.2.5.1 Compressive Strength ....................................................18
2.2.5.1.1 Specimen Preparation and Testing Procedure for Compression Tests on AAC Cubes...................................18
2.2.5.1.2 Compression Test Results for AAC Cubes .............21 2.2.6 Construction of Shear Wall Specimen 17 ...........................................22
2.3 Design and Construction of Shear Wall Specimens 18 and 19....................24 2.3.1 Objectives............................................................................................24 2.3.2 Configurations of Shear Wall Specimen 18 and 19 ............................24 2.3.3 Test Setup for Shear Wall Specimens 18 and 19 ................................27
2.3.3.1 Base Beam......................................................................27 2.3.3.2 Axial Load System .........................................................27 2.3.3.3 Lateral Bracing System ..................................................29 2.3.3.4 Actuators ........................................................................29 2.3.3.5 Instrumentation and Data Acquisition............................30
2.3.3.5.1 Instrumentation........................................................30 2.3.3.5.2 Data Acquisition......................................................33
2.3.4 Loading Protocol .................................................................................34 2.3.5 Material Strengths ...............................................................................34
2.3.5.1 Compressive Strength ....................................................34 2.3.5.1.1 Specimen Preparation and Testing Procedure for
Compression Tests on AAC Cores....................................34 2.3.5.2 Compression Test Results for AAC Cores.....................36 2.3.5.3 Further Comments on Maximum Useful Strain .............38
2.3.6 Splitting Tensile Strength....................................................................41 2.3.6.1 Specimen Preparation and Testing Procedure for
Splitting Tensile Tests on AAC Masonry Units.........................41 2.3.6.2 Splitting Tensile Strength for AAC Units ......................43 2.3.6.3 Comparison between observed and predicted splitting
tensile strength of AAC..............................................................44
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2.3.7 Construction of Shear Wall Specimens 18 and 19..............................46
CHAPTER 3 TEST RESULTS FOR AAC SHEAR WALL SPECIMENS......................50
3.1 Introduction ..................................................................................................50
3.2 Test Results for Shear Wall Specimen 17 ....................................................50 3.2.1 Loading History and Major Events for Shear Wall Specimen 17.......51 3.2.2 Sequence of Crack Formation for Shear Wall Specimen 17...............54
3.2.2.1 Flexural Cracking in Shear Wall Specimen 17 ..............55 3.2.2.2 Flexure-shear cracking in Shear Wall Specimen 17 ......56 3.2.2.3 Additional Cracking in Shear Wall Specimen 17 ..........59 3.2.2.4 Final damage in Shear Wall Specimen 17 .....................60
3.2.3 Load-Displacement Behavior of Shear Wall Specimen 17.................63
3.3 Test Results for Shear Wall Specimen 18 ....................................................64 3.3.1 Loading History and Major Events for Shear Wall Specimen 18.......65 3.3.2 Sequence of Crack Formation for Shear Wall Specimen 18...............68
3.3.2.1 Flexural cracking in Shear Wall Specimen 18 ...............69 3.3.2.2 Web-shear cracking in Shear Wall Specimen 18 ...........70 3.3.2.3 Propagation and Additional Web-shear cracking in
Shear Wall Specimen 18 ............................................................72 3.3.2.4 Final damage in Shear Wall Specimen 18 .....................73
3.3.3 Load-Displacement Behavior for Shear Wall Specimen 18 ...............77
3.4 Shear Wall Specimen 19 ..............................................................................78 3.4.1 Loading History and Major Events for Shear Wall Specimen 19.......79 3.4.2 Sequence of Crack Formation for Shear Wall Specimen 19...............82
3.4.2.1 Flexural cracking in Shear Wall Specimen 19 ...............83 3.4.2.2 Web-shear cracking in Shear Wall Specimen 19 ...........84 3.4.2.3 Propagation and Additional Web-shear cracking in
Shear Wall Specimen 19 ............................................................87 3.4.2.4 Final damage in Shear Wall Specimen 19 .....................88
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3.4.3 Load-Displacement Behavior for Shear Wall Specimen 19 ............... 91
CHAPTER 4 SIGNIFICANCE OF TEST RESULTS ...................................................93
4.1 Review of Behavior Modes for AAC Shear Walls ......................................93 4.1.1 Flexural Cracking................................................................................93 4.1.2 Web-shear cracking.............................................................................95 4.1.3 Flexure-shear cracking ........................................................................97 4.1.4 Nominal Flexural Capacity .................................................................99 4.1.5 Crushing of the Diagonal Strut..........................................................101 4.1.6 Sliding Shear .....................................................................................104
4.2 Hysteretic Behavior of Shear Wall Specimens ..........................................106 4.2.1 Hysteretic Behavior of Flexure-Dominated Specimens....................106 4.2.2 Hysteretic Behavior of Shear-Dominated Specimens .......................116
4.2.2.1 Shear Wall Specimen 18 ..............................................117 4.2.2.2 Shear Wall Specimen 19 ..............................................122 4.2.2.3 Summary of Results for Shear Wall Specimens 18
and 19 ...................................................................................... 126
CHAPTER 5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS.................131
5.1 Summary .................................................................................................131
5.2 Conclusions ................................................................................................132
5.3 Recommendations for Future Work........................................................... 134
APPENDIX A DESIGN PROVISIONS FOR REINFORCED AAC SHEAR WALLS ...136
A.1 Design of AAC Shear Walls ......................................................................136 A.1.1 Web-shear Cracking..........................................................................140 A.1.2 Flexure-Shear Cracking for AAC Shear Walls .................................148 A.1.3 Crushing of the Diagonal Strut..........................................................155 A.1.4 Sliding Shear Capacity ......................................................................160 A.1.5 Nominal Flexural Capacity ...............................................................169
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A.2 Special Provisions for Vertical Panel Construction ...................................171 A.2.1 Prediction of Flexural and Shear Capacities for AAC Shear Walls
with Vertically Oriented Panels ........................................................173 A.2.2 Verification of Shear Capacity for Vertical-Panel Shear Walls
Tested at UT Austin ..........................................................................176 A.2.3 Special Provisions to Avoid Longitudinal Cracking at the Location
of Vertical Reinforcement .................................................................178 A.2.4 Formation of Cracks along Longitudinal Bars in AAC Shear Walls 179 A.2.5 Analysis to Determine if Longitudinal Cracks Formed Prior to
Yielding 182 A.2.6 Implications of the Formation of Longitudinal Cracks.....................186 A.2.7 Analysis of Maximum Permissible Area Ratio if Longitudinal
Reinforcement Remains Elastic ........................................................188 A.2.8 Analysis of the Maximum Permissible Area Ratio in a Plastic
Hinge Zone........................................................................................193
A.3 Design Examples........................................................................................193 A.3.1 Design of an AAC shear wall............................................................193
A.3.1.1 Flexural capacity .........................................................194 A.3.1.2 Shear capacity..............................................................196
A.3.2 Design an AAC Shear Wall for Out-of-plane loads..........................198 A.3.2.1 Flexural capacity .........................................................199 A.3.2.2 Shear capacity.............................................................. 202
APPENDIX B ACI 523.5R-XX GUIDE FOR USING AUTOCLAVED AERATED CONCRETE PANELS ....................................................................................203
B.1 Introduction ................................................................................................203 B.1.1 Definition of Autoclaved Aerated Concrete......................................203 B.1.2 Typical Mechanical and Thermal Characteristics of AAC ...............204 B.1.3 Historical Background of AAC.........................................................205 B.1.4 Applications of AAC Panels .............................................................206 B.1.5 Scope and Objectives of this Guide ..................................................206
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B.2 TYPICAL Materials and Manufacture OF AAC .......................................208 B.2.1 Materials Used in AAC .....................................................................208 B.2.2 Manufacture of AAC.........................................................................208
B.2.2.1 Preparation, Batching and Mixing of Raw Materials ..208 B.2.2.2 Casting, Expansion and Initial Hydration....................209 B.2.2.3 Cutting .........................................................................210 B.2.2.4 Autoclaving .................................................................211 B.2.2.5 Packaging.....................................................................212 B.2.2.6 AAC Strength Classes .................................................213
B.2.3 Typical Dimensions of AAC Units ...................................................214 B.2.3.1 Plain AAC Wall Units .................................................214 B.2.3.2 Reinforced AAC Units ................................................215
B.2.4 Dimensional Tolerances ....................................................................216 B.2.5 Identification and Marking of AAC Units ........................................216
B.3 Structural Design of Reinforced AAC Elements .......................................217 B.3.1 Introductory Remarks regarding Design Provisions .........................217 B.3.2 Proposed Design Provisions for Reinforced AAC Panels ................218
B.3.2.1 Basic Design Assumptions ..........................................218 B.3.2.2 Combinations of Flexure and Axial Load ...................219 B.3.2.3 Bond and Development of Reinforcement ..................219 B.3.2.4 Shear ............................................................................220 B.3.2.5 Bearing.........................................................................221
B.4 Handling, Erection and Construction With AAC Units .............................222 B.4.1 Handling of AAC Panels...................................................................222 B.4.2 Erection of AAC Wall Panels ...........................................................222
B.4.2.1 Erection of AAC Cladding Systems............................222 B.4.2.2 Erection of Vertical AAC Panels for Bearing-Wall
Systems.....................................................................................223 B.4.3 Erection of AAC Floor and Roof Panels...........................................224
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B.4.4 Electrical and Plumbing Installations in AAC ..................................224 B.4.5 Exterior Finishes for AAC ................................................................225
B.4.5.1 Polymer-Modified Stuccos, Paints or Finish Systems.225 B.4.5.2 Masonry Veneer ..........................................................225 B.4.5.3 Finishes for Basement Walls .......................................225
B.4.6 Interior Finishes for AAC Panels ......................................................226 B.4.6.1 Interior Plasters............................................................226 B.4.6.2 Gypsum Board.............................................................226 B.4.6.3 High-Durability Finishes for Commercial
Applications .............................................................................226 B.4.6.4 Ceramic Tile ................................................................ 227
References………………………………………………………………………228 Vita……...………………………………………………………………………230
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List of Tables
Table 2.1 Description of instrumentation used in Shear Wall Specimen 17........14
Table 2.2 Dry weights of AAC cubes measured at Babb and at UT Austin ........20
Table 2.3 Results of compressive strength tests performed at UT Austin ...........22
Table 2.4 Results of compressive strength tests performed at the Babb plant.....22
Table 2.5 Description of instrumentation used in Shear Wall Specimens 18 and
19...................................................................................................................31
Table 2.6 Summary of results of moisture content measured in the cores drilled
for the compressive test (Babb 3 material)....................................................35
Table 2.7 Results of compressive strength tests performed at UT Austin ...........37
Table 2.8 Summary of mean maximum useful strains obtained in this study and
Tanner (2003) ................................................................................................38
Table 2.9 Material properties of this study versus those of Tanner (2003) .........40
Table 2.10 Measured moisture contents (Babb 3 material) .................................42
Table 2.11 Results of splitting tensile strength tests performed at UT Austin.....44
Table 3.1 Load Points, maximum load and drift ratios for each cycle for Shear
Wall Specimen 17 .........................................................................................54
Table 3.2 Description of major events for Shear Wall Specimen 17 ...................55
Table 3.3 Load Points, maximum load drift ratios for each cycle for Shear Wall
Specimen 18 ..................................................................................................68
Table 3.4 Description of major events for Shear Wall Specimen 18 ...................69
Table 3.5 Load Points, maximum load and drift ratios for each cycle for Shear
Wall Specimen 19 .........................................................................................82
Table 3.6 Description of major events for Shear Wall Specimen 19 ...................83
Table 4.1 Observed versus predicted flexural cracking capacities .......................95
Table 4.2 Observed versus predicted web-shear cracking capacities ...................97
Table 4.3 Observed versus predicted flexure-shear cracking capacities...............99
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Table 4.4 Observed versus predicted values for nominal flexural capacity........101
Table 4.5 Observed versus predicted capacities as governed by crushing of the
diagonal strut ...............................................................................................103
Table 4.6 Maximum displacements, ductilities and drift ratios for Shear Wall
Specimen 17 ................................................................................................112
Table 4.7 Comparison of initial tangent and backbone stiffnesses for flexure-
dominated specimens ..................................................................................113
Table 4.8 Comparison of secant stiffnesses after flexural cracking for flexure-
dominated specimens ..................................................................................113
Table 4.9 Comparison of unloading stiffnesses after yield of flexural
reinforcement in the south and north direction for flexure-dominated
specimens ....................................................................................................114
Table 4.10 Comparison of stiffnesses after yield of flexural reinforcement for
flexure-dominated specimens......................................................................115
Table 4.11 Maximum useful displacement drift ratios and ductilities for flexure-
dominated specimens ..................................................................................115
Table 4.12 Observed initial tangent and backbone stiffnesses for shear-dominated
specimens ....................................................................................................127
Table 4.13 Secant stiffnesses after flexural cracking for shear-dominated
specimens ....................................................................................................128
Table 4.14 Unloading stiffnesses after web shear cracking in the south and north
direction for shear-dominated specimens....................................................129
Table 4.15 Strength ratios after web shear cracking and corresponding
displacement ratios for shear-dominated specimens...................................130
Table A.1 Details of shear wall specimens tested at UT Austin .........................138
Table A.2 Details of shear wall specimens tested by Hebel (Germany).............139
Table A.3 Initial predictions of capacity as governed by web-shear cracking for
fully mortared specimens ............................................................................142
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Table A.4 Initial predictions of capacity as governed by web-shear cracking for
partially mortared specimens ......................................................................143
Table A.5 Prediction of capacity as governed by web-shear cracking for fully
mortared specimens (Equation (A.1)) using tested compressive strength ..146
Table A.6 Prediction of capacity as governed by web-shear cracking for
unmortared head joints (Equation (A.2)) using tested compressive strength
.....................................................................................................................146
Table A.7 Results for flexure-shear cracking of AAC flexure-dominated shear
wall specimens ............................................................................................151
Table A.8 Results for flexure-shear cracking of AAC flexure-dominated shear
wall specimens using tensile bond strength of material ..............................152
Table A.9 Predicted shear wall capacities as governed by crushing of the diagonal
strut..............................................................................................................159
Table A.10 Observed versus predicted nominal shear capacities based on nominal
flexural capacity ..........................................................................................171
Table A.11 Observed versus predicted nominal shear capacities based on nominal
flexural capacity with strain hardening included ........................................171
Table A.12 Ratio of base shear at formation of vertical cracks to base shear at
expected flexural capacity (including overstrength) in the flexure-dominated
shear wall specimens ...................................................................................179
Table A.13 Ratio of base shear at observed vertical cracking to the nominal
flexural capacity (without overstrength) in flexure-dominated AAC shear
wall specimens ............................................................................................181
Table A.14 Estimation of order of vertical cracking and yielding of longitudinal
reinforcement, based on strain gages ..........................................................184
Table A.15 Calculated stresses in tensile reinforcement based on elastic theory for
vertical cracks on the south and north sides of the specimen......................186
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Table B.1 Typical mechanical and thermal characteristics of AAC ...................205
Table B.2 Material characteristics of AAC in different strength classes ............214
Table B.3 Dimensions of plain AAC wall units..................................................215
Table B.4 Dimensions of reinforced AAC wall units .........................................215
Table B.5 Dimensional tolerances for reinforced AAC units .............................216
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List of Figures
Figure 2.1 Geometry and reinforcement of Shear Wall Specimen 17 ...................8
Figure 2.2 Plan view of Shear Wall Specimen 17 with details of the stainless-
steel spiral ties .................................................................................................9
Figure 2.3 Typical view of base beam used for Shear Wall Specimen 17..........10
Figure 2.4 Typical details of the axial load system used for Shear Wall Specimen
17 ...................................................................................................................11
Figure 2.5 Different views showing details of the lateral bracing system ...........12
Figure 2.6 Actuator connected to Shear Wall Specimen 17.................................13
Figure 2.7 East face of Shear Wall Specimen 17 showing locations of
instrumentation..............................................................................................15
Figure 2.8 West face of Shear Wall Specimen 17 showing locations of
instrumentation..............................................................................................16
Figure 2.9 Typical view of the strain gauge positions in the flexural
reinforcement of Shear Wall Specimen 17....................................................17
Figure 2.10 Machine used to mill faces of AAC cubes .......................................19
Figure 2.11 Typical view of test setup to measure compressive strength...........21
Figure 2.12 Construction details of Shear Wall Specimen 17 .............................23
Figure 2.13 Geometry and reinforcement of Shear Wall Specimen 18 ...............25
Figure 2.14 Geometry and reinforcement of Shear Wall Specimen 19 ...............26
Figure 2.15 Typical details of modular blocks used in Shear Wall Specimens 18
and 19 ............................................................................................................26
Figure 2.16 Typical details of the axial load system used for Shear Wall
Specimen 18 ..................................................................................................28
Figure 2.17 Typical details of the axial load system used for Shear Wall
Specimen 19 ..................................................................................................29
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Figure 2.18 East face of Shear Wall Specimen 18 showing locations of
instrumentation..............................................................................................32
Figure 2.19 West face of Shear Wall Specimen 18 showing locations of
instrumentation..............................................................................................33
Figure 2.20 Typical view of the test setup to measure compressive strength ......36
Figure 2.21 Compressive stress versus strain (Babb 3 material) .........................37
Figure 2.22 Maximum useful strain versus compressive strength .......................40
Figure 2.23 Test setup to measure splitting tensile strength ................................43
Figure 2.24 Splitting tensile strength versus tested compressive strength...........46
Figure 2.25 Plan view showing typical details of construction of Shear Wall
Specimen 19 ..................................................................................................47
Figure 2.26 Side view of Shear Wall Specimen 18..............................................48
Figure 2.27 Side view of Shear Wall Specimen 19..............................................49
Figure 3.1 Prediction of behavior for Shear Wall Specimen 17 .........................51
Figure 3.2 Actual loading history for Shear Wall Specimen 17 .........................52
Figure 3.3 Actual tip displacement history for Shear Wall Specimen17 ............53
Figure 3.4 Formation of flexural cracking in Shear Wall Specimen 17..............56
Figure 3.5 Flexure-shear cracks at north end of Shear Wall Specimen 17 .........57
Figure 3.6 Formation of flexural-shear cracks in Shear Wall Specimen 17 .......58
Figure 3.7 Formation of additional flexure-shear cracks, and propagation of
cracks from previous events ..........................................................................60
Figure 3.8 Cracking in Shear Wall Specimen 17 at end of test ..........................61
Figure 3.9 Spalling at the north end of Shear Wall Specimen 17 .......................62
Figure 3.10 Toe crushing north at north end of Shear Wall Specimen 17 ...........63
Figure 3.11 Overall hysteretic behavior of Shear Wall Specimen 17 ..................64
Figure 3.12 Prediction of behavior for Shear Wall Specimen 18 ........................65
Figure 3.13 Actual loading history for Shear Wall Specimen 18 ........................66
Figure 3.14 Actual tip displacement history for Shear Wall Specimen 18 ..........67
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Figure 3.15 Formation of flexural cracking in Shear Wall Specimen 18.............70
Figure 3.16 Web-shear cracking at north end of Shear Wall Specimen 18 .........71
Figure 3.17 Web-shear cracking in Shear Wall Specimen 18..............................72
Figure 3.18 Propagation and formation of additional web-shear cracks in Shear
Wall Specimen 18 .........................................................................................73
Figure 3.19 Additional web-shear cracking and toe crushing in Shear Wall
Specimen 18 ..................................................................................................75
Figure 3.20 Web-shear cracks in Shear Wall Specimen 18 .................................76
Figure 3.21 Toe crushing at the north end of Shear Wall Specimen 18 ..............77
Figure 3.22 Overall hysteretic behavior of Shear Wall Specimen 18 ..................78
Figure 3.23 Prediction of behavior for Shear Wall Specimen 19 ........................79
Figure 3.24 Actual loading history for Shear Wall Specimen 19 ........................80
Figure 3.25 Actual tip displacement history for Shear Wall Specimen 19 ..........81
Figure 3.26 Flexural cracks in Shear Wall Specimen 19 .....................................84
Figure 3.27 Web-shear cracking in Shear Wall Specimen 19..............................85
Figure 3.28 Web-shear cracking in Shear Wall Specimen 19..............................86
Figure 3.29 Propagation and formation of additional web-shear cracks along with
some flexure-shear cracks in Shear Wall Specimen 19 ................................88
Figure 3.30 Additional web-shear cracking and toe crushing in Shear Wall
Specimen 19 ..................................................................................................89
Figure 3.31 Web-shear cracking in Shear Wall Specimen 19 at the end of the test
.......................................................................................................................90
Figure 3.32 Toe crushing at the north end of Shear Wall Specimen 19 ..............91
Figure 3.33 Overall hysteretic behavior of Shear Wall Specimen 19 ..................92
Figure 4.1 Typical flexural cracking ....................................................................94
Figure 4.2 Typical web-shear cracking ................................................................96
Figure 4.3 Typical flexure-shear cracking ...........................................................98
Figure 4.4 Strain and force distribution in an AAC shear wall..........................100
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Figure 4.5 Diagonal cracks and crushing of the diagonal strut ..........................102
Figure 4.6 Sliding-shear cracking ......................................................................104
Figure 4.7 Shear friction.....................................................................................105
Figure 4.8 Initial tangent and backbone stiffness for Shear Wall Specimen 17107
Figure 4.9 Stiffness after flexural cracking for Shear Wall Specimen 17.........108
Figure 4.10 Unloading stiffnesses after yielding of the flexural reinforcement for
Shear Wall Specimen 17 .............................................................................109
Figure 4.11 Stiffnesses after yielding of the flexural reinforcement for Shear Wall
Specimen 17 ................................................................................................110
Figure 4.12 Selected drift ratios for Shear Wall Specimen 17...........................111
Figure 4.13 Initial tangent and backbone stiffnesses for Shear Wall Specimen 18
.....................................................................................................................117
Figure 4.14 Secant stiffnesses after flexural cracking for Shear Wall Specimen 18
.....................................................................................................................118
Figure 4.15 Unloading stiffnesses after web shear cracking for Shear Wall
Specimen 18 ................................................................................................119
Figure 4.16 Maximum applied load after web shear cracking in the south and
north directions for Shear Wall Specimen 18 .............................................120
Figure 4.17 Load- displacement response of Shear Wall Specimen 18..............121
Figure 4.18 Initial tangent and backbone stiffnesses for Shear Wall Specimen 19
.....................................................................................................................122
Figure 4.19 Secant stiffnesses after flexural cracking for Shear Wall Specimen 19
.....................................................................................................................123
Figure 4.20 Unloading stiffnesses after web-shear cracking for Shear Wall
Specimen 19 ................................................................................................124
Figure 4.21 Maximum applied load after web-shear cracking in the south and
north directions for Shear Wall Specimen 19 .............................................125
Figure 4.22 Load-displacement response of Shear Wall Specimen 19...............126
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Figure A.1 Test set up for shear wall specimens (UT Austin) ...........................137
Figure A.2 Test setup for shear wall specimens at Hebel (Germany).................139
Figure A.3 Ratios of observed to predicted (Equation (A.6)) web-shear cracking
capacities for AAC shear-wall specimens with fully mortared head joints 144
Figure A.4 Ratios of observed to predicted (Equation (A.6)) web-shear cracking
capacities for AAC shear-wall specimens with partially mortared head joints
.....................................................................................................................145
Figure A.5 Observed versus predicted capacities as governed by web-shear
cracking (Equation (A.1) and Equation (A.2)) using tested compressive
strength ........................................................................................................147
Figure A.6 Observed versus predicted capacities as governed by web-shear
cracking (Equation (A.1)) and Equation (A.2)) using specified compressive
strength ........................................................................................................147
Figure A.7 Flexure-shear cracking......................................................................148
Figure A.8 Hysteretic behavior of Shear Wall Specimen 13 before and after
flexure-shear cracking .................................................................................153
Figure A.9 Hysteretic behavior of Shear Wall Specimen 14b before and after
flexure-shear cracking .................................................................................153
Figure A.10 Hysteretic behavior of Shear Wall Specimen 15a before and after
flexure-shear cracking .................................................................................154
Figure A.11 Hysteretic behavior of Shear Wall Specimen 15b before and after
flexure-shear cracking .................................................................................154
Figure A.12 Hysteretic behavior of Shear Wall Specimen 16 before and after
flexure-shear cracking .................................................................................155
Figure A.13 Diagonal compressive strut in an AAC shear wall .........................156
Figure A.14 External forces acting on an AAC shear wall .................................156
Figure A.15 Forces acting on diagonal strut in an AAC shear wall....................157
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Figure A.16 Formation of bed-joint crack in an AAC shear wall with horizontal
panels...........................................................................................................160
Figure A.17 Sliding shear mechanism in an AAC shear wall with horizontal
panels...........................................................................................................161
Figure A.18 Internal lateral forces generated by dowel action along plane of
sliding shear mechanism .............................................................................162
Figure A.19 Internal lateral forces generated by friction along plane of sliding for
sliding shear mechanism .............................................................................162
Figure A.20 Hysteretic behavior of Two-story Assemblage Specimen..............164
Figure A.21 Base shear and sliding shear capacity versus Load Point for Two-
story Assemblage Specimen........................................................................164
Figure A.22 Hysteretic behavior of Shear Wall Specimen 4 ..............................166
Figure A.23 Base shear and sliding shear capacity versus Load Point for Two-
Story AAC Assbemblage Specimen ...........................................................167
Figure A.24 Base shear and reduced sliding shear capacity versus Load Point for
Two-story Assemblage Specimen...............................................................168
Figure A.25 Equilibrium of an AAC shear wall at nominal flexural capacity....169
Figure A.26 Formation of first diagonal crack in Shear Wall Specimen 2 .........172
Figure A.27 Formation of additional cracks in Shear Wall Specimen 2.............173
Figure A.28 Behavior of monolithic AAC shear wall ........................................174
Figure A.29 Behavior of individual panel for an AAC shear wall .....................174
Figure A.30 Distribution of axial loads for laterally loaded condition and axially
loaded condition ..........................................................................................175
Figure A.31 Base shear capacity for Shear Wall Specimen 2 considering
individual panel behavior and monolithic wall behavior ............................177
Figure A.32 Base shear capacity for Shear Wall Specimen 2 considering
individual panel behavior, behavior of panel groups and monolithic wall
behavior .......................................................................................................178
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Figure A.33 Ratio of base shear at observed longitudinal crack to base shear at
expected flexural capacity (fs=1.25 fy) ........................................................180
Figure A.34 Ratio of base shear at observed longitudinal crack to base shear at
nominal flexural capacity without overstrength..........................................182
Figure A.35 Loss of end block on compression toe in Shear Wall Specimen 16187
Figure A.36 Loss of end blocks and buckling of compression reinforcement in
Shear Wall Specimen 15b ...........................................................................187
Figure A.37 Free-body diagram of longitudinal bar with all load transferred
through lugs and pressure generated in the surrounding grout ...................189
Figure A.38 Stresses generated perpendicular to a cut along the diameter of a
grouted cell ..................................................................................................191
Figure A.39 Calculation of force corresponding to the splitting tensile stresses
across a section of grout ..............................................................................192
Figure B.1 Cellular structure of AAC .................................................................204
Figure B.2 Examples of AAC structural elements ..............................................207
Figure B.3 Overall steps in manufacture of AAC...............................................209
Figure B.4 Fresh AAC after removal of molds ...................................................210
Figure B.5 Cutting AAC into desired shapes......................................................211
Figure B.6 Autoclaving AAC..............................................................................212
Figure B.7 Packaging of finished AAC units......................................................213
Figure B.8 Bond mechanism of welded-wire fabric in AAC..............................220
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CHAPTER 1 Introduction
1.1 GENERAL
The continuous advancement of construction technology in creating new
materials, design innovations and construction techniques requires the
corresponding development of an adequate technical basis for these advances. In
particular, it is important to study the mechanical characteristics and behavior of
new materials. This is true in particular for autoclaved aerated concrete (AAC), a
new material for the United States.
This study forms one part of an extensive research project produced at the
Ferguson Structural Engineering Laboratory of the University of Texas at Austin
under the sponsorship of the Autoclaved Aerated Concrete Products Association
(AACPA). The overall objective of that study is to develop design provisions for
AAC (including seismic design), and their underlying technical basis.
1.2 SCOPE OF OVERALL STUDY
Research at The University of Texas at Austin has involved the
development of design approaches and corresponding design provisions, and the
verification of those provisions through extensive testing. It has also involved the
development of R and Cd factors for seismic design of AAC structural systems.
The experimental study carried out at The University of Texas at Austin
has consisted of the testing of 19 AAC shear-wall specimens controlled by
different behaviors, and a two-story AAC assemblage specimen. The 19 shear-
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wall specimens were tested to develop and validate the design provisions
proposed for the AAC shear walls. The assemblage was tested to validate the
proposed design and construction provisions on a global level.
1.3 OBJECTIVES OF OVERALL STUDY
Research at The University of Texas at Austin had the following
objectives:
• to determine fundamental material properties of the AAC manufactured in
the United States;
• to develop and verify the design provisions for AAC shear wall
specimens, addressing flexural cracking, web-shear cracking, flexure-
shear cracking, sliding shear, crushing of the diagonal strut, and flexural
capacity;
• to verify the adequacy of proposed construction details for connections
between AAC floor diaphragms and the AAC shear walls;
• to establish the force-reduction factor (R) and displacement-amplification
factor (Cd) for design of AAC structures in seismic zones.
1.4 ORGANIZATION OF OVERALL STUDY
The overall study comprises the following elements:
• the development of the shear-wall test setup and results from pilot
specimens, carried out by Matthew Brightman, Jennifer Tanner and Jorge
Varela, and described in the MS thesis of Brightman (Brightman 2000);
• the development of design provisions for AAC structural systems, carried
out by Jennifer Tanner and Jorge Varela, and additionally by Jaime
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Argudo, and described in the PhD dissertation of Tanner (2003) and the
MS thesis of Argudo (2003);
• the development of R and Cd factors, carried out by Jorge Varela, and
described in his PhD dissertation;
• the synthesis of material testing data, carried out by Jennifer Tanner and
Jaime Argudo, and described in the PhD dissertation of Tanner (2003) and
the MS thesis of Argudo; and
• confirmation of the applicability of previously developed shear-wall
provisions to low-strength AAC shear walls, carried out by Ulises Cancino
and Jorge Varela, and described in this MS thesis by Cancino (2003).
1.5 SCOPE OF THESIS
The purpose of the study described in this thesis was to conduct and
evaluate the results of reversed cyclic load tests on the final 3 of 19 AAC shear
wall specimens. The three AAC specimens (SWS17, SWS18 and SWS19) were
constructed with vertically oriented, reinforced panels (SWS17) or masonry-type
units (SWS18 and SWS19). The tests described here were intended to evaluate
the in-plane behavior of those low-strength AAC shear walls, and to validate the
applicability to such walls, of previously developed design provisions.
Shear Wall SWS17 was designed to exhibit flexure-dominated behavior.
Because the behavior of flexure-dominated walls is well understood, the main
purpose of this study was to evaluate improvements in behavior of specimens
constructed with spiral ties devices connecting the extreme-fiber elements to the
remainder of the wall.
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Shear Walls SWS18 and SWS19 were constructed with low-strength AAC
material, and were intended to exhibit shear-dominated behavior. They were
tested to confirm the applicability to low-strength AAC of previously developed
provisions for shear capacity.
1.6 OBJECTIVES OF THESIS
The study described here had the following specific objectives:
• to examine the behavior of the compression toes as influenced by
larger grout columns at each end and by the use of stainless steel
spiral ties to attach the end blocks to the rest of the wall (SWS17);
• to examine the general hysteretic behavior of the specimens and
compare observed story drift and displacement ductility with
analytical assumptions (SWS17);
• to validate previously proposed design provisions for AAC shear
walls (SWS17);
• to validate the previously proposed design provisions for web-
shear cracking, in the case of low-compressive strength AAC
(SWS18 and SWS19); and
• to validate the similarity between the overall hysteretic behavior of
shear-dominated low-strength AAC shear walls (SWS18 and
SWS19), and the shear walls previously tested at UT Austin.
• to validate the similarity between the overall hysteretic behavior of
flexure-dominated low-strength AAC shear walls (SWS17), and
the shear walls previously tested at UT Austin.
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1.7 ORGANIZATION OF THIS THESIS
This thesis is organized as follows: Chapter 2 presents the characteristics
of the three AAC shear wall specimens, mechanical properties of the AAC
material, instrumentation and planning prior to the tests. Chapter 3 contains
information obtained during the tests, including the principal observations and
basic behavior of the specimens. Chapter 4 presents an evaluation of the
significance of the results obtained from the tests. Finally, Chapter 5 provides the
summary, conclusions and recommendations resulting from the study.
Two Appendices are also included:
o Appendix A presents the relevant theory, including the design provisions
for reinforced AAC shear walls developed by Tanner (2003) and Varela
(2003).
o Appendix B presents the first chapters of the current draft of the ACI
523.5 R-xx Guide for Using Autoclaved Aerated Concrete Panels (Argudo
2003). The purpose of this appendix is to present basic information on
AAC, that was not developed by the author.
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CHAPTER 2 Test Specimens, Test Setups, and Testing
Procedures
2.1 INTRODUCTION
The testing program included one flexure-dominated specimen (SWS17)
and two shear-dominated specimens (SWS18 and SWS19), tested using the same
setup and instrumentation used in previous tests by Varela (2003) and Tanner
(2003). The setup permitted the application of constant gravity loads and quasi-
static, reversed cyclic in-plane shear loads to single-story AAC shear walls. The
instrumentation permitted the capture of global behavior (such as displacements
and loads), and local behavior (such as stresses in flexural reinforcement).
The results of the AAC material strengths are also presented. The
specimens were designed using those strengths, and the wall geometry,
reinforcement and axial load were chosen according to the desired mode of
behavior.
In this chapter, the objectives, test setup, instrumentation, material
strengths, design of specimens, loading protocol and construction of the
specimens are presented.
2.2 DESIGN AND CONSTRUCTION OF SHEAR WALL SPECIMEN 17
2.2.1 Objectives
Shear Wall Specimen 17 was tested to verify the previously proposed
design provisions for the case of a flexure-dominated specimen of low-strength
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AAC, and also to evaluate possible improvements in the performance of the wall
through the incorporation of stainless-steel spiral ties between the U-blocks and
the remainder of the wall. This specimen was intended to fail in flexure. With this
intent, the aspect ratio, the axial load and the reinforcement of the specimen were
selected.
2.2.2 Configuration of Shear Wall Specimen 17
The wall measured 112 in. (2.84 m) long by 144 in. (3.66 m) high by 8 in.
(0.203 m) thick. The height from the bottom of the wall to the line of the load
application was 154 in. (3.91 m). The aspect ratio of the wall (height divided by
plan length) was 1.34. Figure 2.1 shows the geometry and reinforcement of Shear
Wall Specimen 17.
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64.0 in (1.63 m)
t = 8 in (0.20 m)
16.5 in(0.42 m)
304.5 in (7.73 m)
112.0 in (2.84 m)
144.0 in (3.66 m)
20.0 in (0.51 m)
# 5 bars
Stainless–steel spiral ties
64.0 in (1.63 m)
t = 8 in (0.20 m)
16.5 in(0.42 m)
304.5 in (7.73 m)
112.0 in (2.84 m)
144.0 in (3.66 m)
20.0 in (0.51 m)
# 5 bars
Stainless–steel spiral ties
Figure 2.1: Geometry and reinforcement of Shear Wall Specimen 17
Figure 2.2 shows a plan view of the masonry-type lintel units (U-blocks)
attached to the vertical panels with the stainless-steel spiral ties, and the geometric
characteristics of the U-blocks.
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grout
Stainless-steel spiral ties Vertical Panels
U-blocks8 in. (0.20 m)
8 in. (0.20 m)
24 in. (0.61 m)Details of U-blocks
8 in. (0.20 m)
grout
Stainless-steel spiral ties Vertical Panels
U-blocks8 in. (0.20 m)
8 in. (0.20 m)
24 in. (0.61 m)Details of U-blocks
8 in. (0.20 m)
Figure 2.2: Plan view of Shear Wall Specimen 17 with details of the stainless-
steel spiral ties
2.2.3 Test Setup for Shear Wall Specimen 17
2.2.3.1 Base Beam
The base beam measured 304.5 in. (7.73 m) long by 64 in. (1.63 m) wide
by 16.5 in. (0.42 m) high. To prevent sliding or uplifting, the base beam was tied
to the reaction floor of the laboratory through post-tensioned rods. Details of the
base beam used for Shear Wall Specimen 17 are shown in Figure 2.3.
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16.5 in(0.42 m)
64.0 in (1.63 m)
Post-Tensioned Rods
304.5 in (7.73 m)
Base beam
Loading beam
16.5 in(0.42 m)
64.0 in (1.63 m)
Post-Tensioned Rods
304.5 in (7.73 m)
Base beam
Loading beam
304.5 in (7.73 m)
Base beam
Loading beam
Figure 2.3: Typical view of base beam used for Shear Wall Specimen 17
2.2.3.2 Axial Load System
The constant axial load of 25 kips (111.2 kN) was applied to the specimen
by a loading beam with a weight of 5 kips (22.24 kN), and by hydraulic actuators
controlled by a load maintainer that provided 20 kips (89 kN). The axial load
from the load maintainer was transmitted through two threaded rods, one at each
side of the specimen, and located at the center of the wall. These threaded rods
were connected at the top with a steel swivel beam and to the bottom with a
swivel steel box which was tied to the base beam with post-tensioned rods. Figure
2.4 shows the axial load system for Shear Wall Specimen 17.
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Threaded Rod
Swivel beam
Spreader beam
Swivel Box Actuator
Load Maintainer
Threaded Rod
Swivel beam
Spreader beam
Swivel Box Actuator
Load Maintainer
Threaded Rod
Swivel beam
Spreader beam
Swivel Box Actuator
Load Maintainer
Figure 2.4: Typical details of the axial load system used for Shear Wall
Specimen 17
2.2.3.3 Lateral Bracing System
The lateral bracing system, necessary to provide out-of-plane stability to
the specimen, consisted of four steel cables connected to the loading beam of the
specimen at four different points. Two of these cables were attached to the
reaction wall, and the other two were attached to steel columns (Figure 2.5).
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Reaction Wall
Wall
Steel Column
Chains
CablesCables
Plan View Elevation
Rea
ctio
n W
all
Wal
l
Stee
l Col
umn
Stee
l Col
umn
Reaction Wall
Wall
Steel Column
Chains
CablesCables
Plan View Elevation
Rea
ctio
n W
all
Wal
l
Stee
l Col
umn
Stee
l Col
umn
Figure 2.5: Different views showing details of the lateral bracing system
2.2.3.4 Actuators
Horizontal load was applied to the specimen with a 60 kips (270 kN)
hydraulic actuator, controlled by an air-operated pump. The actuator has a
maximum extension of 18.0 in. (0.46 m). Figure 2.6 shows the actuator connected
to the loading beam of Shear Wall Specimen 17.
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N
Actuator
Air-operated Pump
NN
Actuator
Air-operated Pump
Figure 2.6: Actuator connected to Shear Wall Specimen 17
2.2.3.5 Instrumentation and Data Acquisition
2.2.3.5.1 Instrumentation
The global and local behavior of the specimen was verified through
specific instruments to measure pressure, force and displacement. The types of
instruments used include: pressure transducers, load cells, force washers, linear
potentiometers, and string potentiometers. Table 2.1 describes the instrumentation
used in Shear Wall Specimen 17. Figure 2.7 and Figure 2.8 show the location of
those instruments on the specimen.
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Table 2.1: Description of instrumentation used in Shear Wall Specimen 17
Instrument Label
Kind of
Behavior
Measurement
Type of
Measurement
Output
reading
on the
instrument
Units
used
in
output
file
String pot. SP1 Local Behavior Vertical displ. Length in.
String pot. SP2 Local Behavior Vertical displ. Length in.
String pot. SP3 Local Behavior Vertical displ. Length in.
String pot. SP4 Local Behavior Vertical displ. Length in.
String pot. SP5 Local Behavior Vertical displ. Length in.
String pot. SP6 Local Behavior Vertical displ. Length in.
String pot. SP7 Local Behavior Diagonal displ. Length in.
String pot. SP8 Local Behavior Diagonal displ. Length in.
String pot. SP9 Global Behavior Vertical displ. Length in.
String pot. SP10 Global Behavior Vertical displ. Length in.
String pot. SP11 Global Behavior Horizontal displ. Length in.
String pot. SP12 Global Behavior Horizontal displ. Length in.
Linear pot. LP1 Local Behavior Found.-floor slip Length in.
Linear pot. LP2 Local Behavior Wall-L.Beam slip Length in.
Linear pot. LP3 Local Behavior Wall-L.Beam slip Length in.
Linear pot. LP4 Local Behavior Wall-Found. slip Length in.
Load Cell LC Global Behavior Force in ram Force kips
Force Washer FW Local Behavior Force in rods Force kips
Pressure Trans PT1 Global Behavior Pressure in ram Pressure ksi
Pressure Trans PT2 Global Behavior Pressure in ram Pressure ksi
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N
SP1SP2
SP3
SP4SP5
SP6
SP7 SP8
SP12
LP1
LP2
LP4
Reaction Wall
Actuator
Figure 2.7: East face of Shear Wall Specimen 17 showing locations of
instrumentation
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16
N
Reaction wall
Actuator
SP9 SP10
SP11LP3
FW
LC
Figure 2.8: West face of Shear Wall Specimen 17 showing locations of
instrumentation
Additionally, three strain gauges were attached to each flexural reinforcing
bar at three different levels within the bottom 8 in. (200 mm). These strain gauges
measured the stress induced in the flexural reinforcement during the application
of the horizontal force (Figure 2.9).
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SG 1
SG 2
SG 37.87 in. (200 m m )
Strain G auges (SG )
Reinforcem ent bar
SG 1
SG 2
SG 37.87 in. (200 m m )
Strain G auges (SG )
Reinforcem ent bar
Figure 2.9: Typical view of the strain gauge positions in the flexural
reinforcement of Shear Wall Specimen 17
2.2.3.5.2 Data Acquisition
The instruments were connected to a full-bridge, and the strain gauges, to
a quarter-bridge box. The full-bridge box was excited with 10 volts and the
quarter-bridge box with 2 volts, both were provided by a precision power supply.
These bridge boxes were connected to a HP3852A scanner. Analog-to-digital
conversion was carried out by a National Instruments card in a Windows-based
microcomputer running MS Excel 7.0.
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2.2.4 Loading Protocol
The lateral loading program consisted of reversed cycles to a
monotonically increasing maximum load or displacement. Prior to starting the
tests, an initial cycle of low-lateral load, normally 5 kips (22.5 kN), was applied to
every specimen to check the complete setup (loading equipment, lateral bracing,
instruments and data acquisition). Initial loading cycles were applied under load
control to load levels predicted to produce major events in the shear-wall
specimens tested. Subsequent loading cycles were applied under displacement
control. For Shear Wall Specimen 17, the loading history was switched from load
to displacement control after yield of flexural reinforcement.
2.2.5 Material Strengths
2.2.5.1 Compressive Strength
Shear Wall Specimen 17 was constructed using AAC material
corresponding to Class PAAC4, which has a specified compressive strength of 4
MPa (580 psi). The compressive strength of the AAC material in that specimen
was tested for compliance with that specified strength.
2.2.5.1.1 Specimen Preparation and Testing Procedure for Compression
Tests on AAC Cubes
Cubes for the compressive tests were prepared from the AAC material
used to construct Shear Wall Specimen 17. This material had been shipped to UT
from Babb International, Inc. (Adel, GA). In this thesis, it is designated “Babb
4.”
Nine cubes were prepared at the Babb plant for testing according to
ASTM C1386. The cubes were removed from AAC blocks using a dry circular
saw to extract roughly cubical blocks of AAC. These blocks were then cut into 4-
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in. (100 mm) cubes using a water-cooled circular saw. All cubes were oriented so
that they would be tested perpendicular to the direction of rise.
All faces of the AAC cubes were milled using a machine with two
grinding wheels that allowed milling two parallel faces of the cubes at the same
time (Figure 2.10).
Figure 2.10: Machine used to mill faces of AAC cubes
After the cubes were milled, their moisture content was measured by
weighing. Because that moisture content exceeded the maximum value specified
in ASTM C1386, the cube specimens were placed in an oven for 24 hours at a
constant temperature of 140 degrees Fahrenheit. After that time, the cubes were
again weighed. The weights of AAC cubes measured at Babb Plant and at UT
Austin are presented in Table 2.2.
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Table 2.2: Dry weights of AAC cubes measured at Babb and at UT Austin
Material Block Number
Weight (after oven)
at Babb
lb (kg)
Weight (after oven)
at UT Austin
lb (kg)
Ratio of the
Weight at Babb
to Weight at UT
Austin Babb 4 1-1 1.51 (0.6873) 1.48 (0.6707) 1.02 Babb 4 1-2 1.45 (0.6594) 1.43 (0.6478) 1.01 Babb 4 1-3 1.44 (0.6565) 1.42 (0.6440) 1.01 Babb 4 1-4 1.42 (0.6470) 1.42 (0.6450) 1.00 Babb 4 1-5 1.39 (0.6300) 1.38 (0.6294) 1.00 Babb 4 1-6 1.38 (0.6280) 1.38 (0.6256) 1.00
Three cubes were tested at the Babb plant laboratory, and the rest were
sent to UT Austin for confirmatory compressive strength tests (Varela 2003).
Compression testing was performed in a universal machine, which includes a load
cell and a spherical seat to apply uniform load. Data were recorded using data-
acquisition software of the Ferguson Structural Engineering Laboratory of UT
Austin. Figure 2.11 shows the test setup used in the compressive tests.
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Figure 2.11: Typical view of test setup to measure compressive strength
2.2.5.1.2 Compression Test Results for AAC Cubes
Compressive-strength results for the six specimens tested at UT Austin,
summarized in Table 2.3, ranged from 737 psi (5.08 MPa) to 944 psi (6.51 MPa),
with a final average of 811 psi (5.59 MPa), and a COV of 9.33 %. Compressive-
strength results for the three specimens tested at the Babb plant laboratory are
summarized in Table 2.4. The moisture content of the cubes complied with the
range of 5 % to 15 % specified by ASTM C1386.
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Table 2.3: Results of compressive strength tests performed at UT Austin
Material Cube AACf
psi (MPa)
Duration
of Test
(seconds)
Average
psi (MPa)
COV
(%)
Average
psi (MPa)
COV
(%)
Babb 4 1-1 811 (5.59) 110
Babb 4 1-2 775 (5.34) 110
Babb 4 1-3 737 (5.08) 150
774 (5.30) 4.78
Babb 4 1-4 944 (6.51) 120
Babb 4 1-5 821 (5.66) 120
Babb 4 1-6 866 (5.97) 150
877 (6.0) 7.10
811 (5.59) 9.33
Table 2.4: Results of compressive strength tests performed at the Babb plant
Material Cube AACf
psi (MPa)
Duration
of Test
(seconds)
Average
psi (MPa)
COV
(%)
Babb 4 1-7 870 (6.00) 60
Babb 4 1-8 769 (5.30) 110
Babb 4 1-9 740 (5.10) 53
793 (5.50) 8.61
2.2.6 Construction of Shear Wall Specimen 17
The surface of the base beam was roughened and pre-wetted. A leveling
bed was applied, using conventional Portland cement-lime masonry mortar
conforming to ASTM C270, Type S by proportion. The vertical panels were set
up and joined with thin-bed mortar, and were clamped together to apply pressure
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to the face of the joints. The plumbness of the panels was checked frequently
during construction. The U-blocks were placed at each end of the wall, and were
joined to the vertical panels using thin-bed mortar and stainless-steel spiral ties.
The cores created by these U-blocks and the vertical panels were filled with
coarse grout conforming to ASTM C476 by proportion and consolidated by
vibrator. Figure 2.12 shows a partial view of Shear Wall Specimen 17 after
construction.
U-blocks
# 5 bars
Thin-bed mortar joints
Vertical panels U-blocks
# 5 bars
Thin-bed mortar joints
Vertical panels
Figure 2.12: Construction details of Shear Wall Specimen 17
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2.3 DESIGN AND CONSTRUCTION OF SHEAR WALL SPECIMENS 18 AND 19
2.3.1 Objectives
Shear Wall Specimens 18 and 19 were tested to verify the previously
proposed design provisions for the case of a shear-dominated specimen of low-
strength AAC, and also to examine the overall hysteretic behavior of the walls.
These specimens were intended to fail in web-shear cracking. With this intent,
their aspect ratio, axial load and flexural reinforcement were selected.
2.3.2 Configurations of Shear Wall Specimen 18 and 19
Shear Wall Specimen 18 was constructed with AAC masonry units placed
in running bond. The wall measured 144 in. (3.66 m) long by 144 in. (3.66 m)
high by 8 in. (0.203 m) thick. The height from the bottom of the wall to the line of
the load application was 154 in. (3.91 m). The aspect ratio of the wall (height
divided by plan length) was 1.07. The threaded rods used as external flexural
reinforcement corresponded to ASTM A193-B7 bars 1 in. (25.4 mm) in diameter.
Figure 2.13 shows the geometry and reinforcement of Shear Wall Specimen 18.
Shear Wall Specimen 19 was constructed with AAC masonry units placed
in running bond. The wall measured 216 in. (5.49 m) long by 144 in. (3.66 m)
high by 8 in. (0.203 m) thick. The height from the bottom of the wall to the line of
the load application was 154 in. (3.91 m). The aspect ratio of the wall (height
divided by plan length) was 0.71. The threaded rods used as external flexural
reinforcement corresponded to ASTM A193-B7 bars 1 in. (25.4 mm) in diameter.
Figure 2.14 shows the geometry and reinforcement of Shear Wall Specimen 19.
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144.0 in (3.66 m)
64.0 in (1.63 m)
t = 8 in (0.20 m)
N
304.5 in (7.73 m)
144.0 in (3.66 m)
16.5 in (0.42 m)
20.0 in (0.51 m)
# 5 bars
144.0 in (3.66 m)
64.0 in (1.63 m)
t = 8 in (0.20 m)
N
304.5 in (7.73 m)
144.0 in (3.66 m)
16.5 in (0.42 m)
20.0 in (0.51 m)
# 5 bars
Figure 2.13: Geometry and reinforcement of Shear Wall Specimen 18
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144.0 in (3.66 m)
64.0 in (1.63 m)
t = 8 in (0.20 m)
# 5 @ 4 ft
N
304.5 in. (7.73 m)
216.0 in (5.49 m)
16.5 in (0.42 m)
20.0 in (0.51 m)
144.0 in (3.66 m)
64.0 in (1.63 m)
t = 8 in (0.20 m)
# 5 @ 4 ft
N
304.5 in. (7.73 m)
216.0 in (5.49 m)
16.5 in (0.42 m)
20.0 in (0.51 m)
Figure 2.14: Geometry and reinforcement of Shear Wall Specimen 19
Figure 2.15 shows the geometric characteristics of the modular blocks
used in Shear Wall Specimens 18 and 19.
24 in.(0.61 m)
8 in. (0.20 m)
8 in.(0.20 m)
24 in.(0.61 m)
8 in. (0.20 m)
8 in.(0.20 m)
Figure 2.15: Typical details of modular blocks used in Shear Wall Specimens
18 and 19
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2.3.3 Test Setup for Shear Wall Specimens 18 and 19
2.3.3.1 Base Beam
The foundation used for Shear Wall Specimens 18 and 19 was a base
beam with identical geometric characteristics to that of the base used for Shear
Wall Specimen 17.
2.3.3.2 Axial Load System
An axial load of 45 kips (200.12 kN) was applied to Shear Wall Specimen
18 by a loading beam with a weight of 5 kips (22.24 kN) and four threaded rods
post-tensioned manually which provided 40 kips (177.88 kN) in total. These
threaded rods, two at each end of the specimen, were connected at the top with
transverse steel beams and to the bottom with steel boxes which were tied to the
base beam with bolts (post-tensioned rods). Figure 2.16 shows the axial load
system used for Shear Wall Specimen 18.
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Threaded Rod
Steel beam
Steel Box
Threaded Rod
Steel beam
Steel Box
Figure 2.16: Typical details of the axial load system used for Shear Wall
Specimen 18
An axial load of 58 kips (258 kN) was applied to Shear Wall Specimen 19
by a loading beam with a weight of 8 kips (35.58 kN) and four threaded rods post-
tensioned manually to provide 50 kips (222.40 kN) in total. The setup of these
threaded rods was the same as for Shear Wall Specimen 18. Figure 2.17 shows the
axial load system used for Shear Wall Specimen 19.
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Threaded Rod
Steel beam
Steel Box
Threaded Rod
Steel beam
Steel Box
Steel beam
Steel Box
Figure 2.17: Typical details of the axial load system used for Shear Wall
Specimen 19
2.3.3.3 Lateral Bracing System
The lateral bracing system was necessary to provide out-of-plane stability
to the specimens. The system was identical to that used for Shear Wall Specimen
17.
2.3.3.4 Actuators
The actuator was identical to that used for Shear Wall Specimen 17.
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2.3.3.5 Instrumentation and Data Acquisition
2.3.3.5.1 Instrumentation
The global and local behavior of both specimens was verified through
specific instruments to measure pressure, force and displacement. The types of
instruments used include: pressure transducers, load cells, force washers, linear
potentiometers, and string potentiometers. Table 2.5 describes the instrumentation
used in Shear Wall Specimens 18 and 19. Figure 2.18 and Figure 2.19 show the
location of that instrumentation in Shear Wall Specimen 18. The same
configuration of instrumentation was used in Shear Wall Specimen 19.
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Table 2.5: Description of instrumentation used in Shear Wall Specimens 18 and
19
Instrument Label Kind of Behavior
Measurement
Type of
Measurement
Output
reading on
the
instrument
Units
used in
output
file
String pot. SP1 Local Behavior Vertical displ. Length in.
String pot. SP2 Local Behavior Vertical displ. Length in.
String pot. SP3 Local Behavior Vertical displ. Length in.
String pot. SP4 Local Behavior Vertical displ. Length in.
String pot. SP5 Local Behavior Vertical displ. Length in.
String pot. SP6 Local Behavior Vertical displ. Length in.
String pot. SP7 Local Behavior Diagonal displ. Length in.
String pot. SP8 Local Behavior Diagonal displ. Length in.
String pot. SP9 Global Behavior Vertical displ. Length in.
String pot. SP10 Global Behavior Vertical displ. Length in.
String pot. SP11 Global Behavior Horizontal displ. Length in.
String pot. SP12 Global Behavior Horizontal displ. Length in.
Linear pot. LP1 Local Behavior Found.-floor slip Length in.
Linear pot. LP2 Local Behavior Wall-L.Beam slip Length in.
Linear pot. LP3 Local Behavior Wall-L.Beam slip Length in.
Linear pot. LP4 Local Behavior Wall-Found. slip Length in.
Load Cell LC Global Behavior Force in ram Force kips
Force Washer FW1 Local Behavior Force in rods Force kips
Force Washer FW2 Local Behavior Force in rods Force kips
Force Washer FW3 Local Behavior Force in rods Force kips
Force Washer FW4 Local Behavior Force in rods Force kips
Pressure Trans PT1 Global Behavior Pressure in ram Pressure ksi
Pressure Trans PT2 Global Behavior Pressure in ram Pressure ksi
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Reaction Wall
N
SP12
Actuator
SP4
SP5
SP6
SP1
SP2
SP3
SP7 SP8
LP1
LP2
LP4
FW1 FW2
Reaction Wall
N
SP12
Actuator
N
SP12
Actuator
SP4
SP5
SP6
SP1
SP2
SP3
SP7 SP8
LP1
LP2
LP4
FW1 FW2
SP4
SP5
SP6
SP1
SP2
SP3
SP7 SP8
LP1
LP2
LP4
FW1 FW2
Figure 2.18: East face of Shear Wall Specimen 18 showing locations of
instrumentation
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N
Reaction wall
SP10FW4
Actuator
SP11
LC
SP9FW3
LP3NN
Reaction wall
SP10FW4
Actuator
SP11
LC
Actuator
SP11
LC
SP9FW3
LP3
Figure 2.19: West face of Shear Wall Specimen 18 showing locations of
instrumentation
Additionally, two strain gauges were attached to each extreme flexural
reinforcing bar at two different levels within the bottom 4 in. (100 mm). These
strain gauges measured the stress induced in the flexural reinforcement during the
application of the horizontal force. The strain-gauge positions in Shear Wall
Specimens18 and 19 were similar to those used in Shear Wall Specimen 17.
2.3.3.5.2 Data Acquisition
The data acquisition system and connection of the instrumentation used in
Shear Wall Specimens 18 and 19 were the same as those used for Shear Wall
Specimen 17.
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2.3.4 Loading Protocol
The lateral loading program used for Shear Wall Specimens 18 and 19 was
similar to that used for Shear Wall Specimen 17. For the shear-dominated
specimens, the loading history was switched from load to displacement control
after web-shear cracking.
2.3.5 Material Strengths
2.3.5.1 Compressive Strength
Shear Wall Specimens 18 and 19 were constructed using AAC material
corresponding to Class PAAC2, which has a specified compressive strength of 2
MPa (290 psi). The compressive strength of the AAC material in those specimens
was tested for compliance with that specified strength, using cubes prepared at the
Babb plant and cores taken from masonry type units at UT Austin.
2.3.5.1.1 Specimen Preparation and Testing Procedure for Compression
Tests on AAC Cores
Cores for the compressive tests were prepared from the AAC material
used to construct Shear Wall Specimen 18 and 19. This material had been shipped
to UT from Babb International, Inc. (Adel, GA). In this thesis, that material is
designated “Babb 3.”
Nine cores were prepared at UT for testing according to the same protocol
prescribed for testing cubes in ASTM C1386. The cores were removed from the
center and the outer third of AAC units, and measured 16137 in. (198 mm) long
by 16113 in. (94 mm) in diameter. Their aspect ratio (length divided by diameter)
was 2.
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After the cores were extracted, their weight, density and moisture contents
were measured. The moisture content of the cores must be between 5 % and 15 %
according to ASTM C1386. The moisture content (MC) was measured three
times: at the time of the compressive test; at the end of the test; and five days after
the end of the test as a confirmation of the dry density. Table 2.6 shows the
moisture content recorded from the cores.
Table 2.6: Summary of results of moisture content measured in the cores drilled
for the compressive test (Babb 3 material)
Immediately before the Test Immediately after the Test 5 days after the Test
Core Meausred
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
Measured
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
Measured
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
1-1 34.10 30.09 13.33 34.10 30.09 13.33 31.61 30.09 5.05
1-2 33.27 30.09 10.57 32.86 30.09 9.21 30.57 30.09 1.60
1-3 32.86 30.09 9.21 32.44 30.09 7.81 30.57 30.09 1.60
2-1 33.69 30.09 11.96 34.50 30.09 14.66 31.82 30.09 5.75
2-2 32.02 30.09 6.41 N.A 30.09 N.A N.A 30.09 N.A
2-3 32.02 30.09 6.41 32.02 30.09 6.41 30.15 30.09 0.2
3-1 31.61 30.09 5.05 31.61 30.09 5.05 30.15 30.09 0.2
3-2 33.27 30.09 10.57 32.86 30.09 9.21 30.78 30.09 2.29
3-3 33.69 30.09 11.96 33.27 30.09 10.57 30.78 30.09 2.29
The compressive test setup included an extensometer attached to a linear
potentiometer with a 2-inch range of measuring the axial deformation during the
test. The test was performed in a universal testing machine, which includes a load
cell and a spherical head to apply uniform load to cores. Data were recorded using
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data-acquisition software of the Ferguson Structural Engineering Laboratory of
UT Austin. Figure 2.20 shows the test setup used in the compressive tests.
Figure 2.20: Typical view of the test setup to measure compressive strength
2.3.5.2 Compression Test Results for AAC Cores
Compressive strengths for the six cores, summarized in Table 2.7, ranged
from 287 psi (1.99 MPa) to 370 psi (2.57 MPa), with a mean of 344 psi (2.39
MPa) and a COV of 8.13 %. Figure 2.21 shows the stress-strain curves obtained
for the six cores.
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Table 2.7: Results of compressive strength tests performed at UT Austin
Material Core AACf
psi (MPa)
Moisture
Content
(%)
Average
psi (MPa)
COV
(%)
Average
psi (MPa)
COV
(%)
Babb 3 1 350 (2.43) 13.33
Babb 3 2 335 (2.32) 10.57
Babb 3 3 355 (2.46) 9.21
347 (2.41) 2.45
Babb 3 4 370 (2.57) 11.96
Babb 3 5 367 (2.55) 10.57
Babb 3 6 287 (1.99) 6.41
341 (2.37) 11.27
344 (2.39) 8.13
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025
Strain
Stre
ss (k
si)
0.00
0.34
0.69
1.03
1.38
1.72
2.06
2.41
2.75
Stre
ss (M
Pa)
Test Core 1Test Core 2Test Core 3Test Core 4Test Core 5Test Core 6
Figure 2.21: Compressive stress versus strain (Babb 3 material)
The range of maximum strains was less than 0.003, and was also less than
the values reported by Tanner (2003). To investigate this apparent discrepancy,
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the maximum strain values of this study and those of previous studies were
investigated further, and are discussed immediately below.
2.3.5.3 Further Comments on Maximum Useful Strain
Table 2.8 summarizes for each lot of material, the mean maximum useful
strain (εAAC max) reported in this study and the values reported by Tanner (2003).
Figure 2.22 is a graph of those maximum strain values as a function of tested
compressive strength.
Table 2.8: Summary of mean maximum useful strains obtained in this study
and Tanner (2003)
Shipment Study AACf
psi (MPa) εAAC max
Babb 3 Cancino (2003) 0.34 (2.34) 0.0015
Contec 1 Tanner (2003) 0.75 (5.16) 0.0025
Contec 2 Tanner (2003) 0.95 (6.53) 0.0027
Babb 1 Tanner (2003) 1.10 (7.56) 0.0027
Hebel 2 Tanner (2003) 1.30 (8.94) 0.0030
Ytong 2 Tanner (2003) 0.63 (4.33) 0.0026
Babb 2 Tanner (2003) 0.48 (3.3) 0.0020
Figure 2.22 shows a clear tendency for the maximum useful strain of AAC
to decrease with decreasing compressive strength. Results reported in this thesis
for low-strength AAC are consistent with those reported previously by Tanner
(2003).
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In previous work by Tanner (2003), Varela (2003) and Argudo (2003), the
value of εAAC max was reported as a constant 0.003, independent of compressive
strength. Though not used directly in design provisions, εAAC max is indirectly related
to vital behavioral characteristics such as nominal flexural capacity, and the
available ductility and drift capacities used to establish appropriate values of R
and Cd.
Because (εAAC max) is apparently lower for low-strength AAC, the behavior of
structural elements of low-strength AAC must be carefully reviewed to ensure
that previously developed expressions for nominal flexural capacity and ductility
and drift capacity are applicable to low-strength AAC as well. Parenthetically,
one would expect the nominal flexural capacity of AAC elements to be governed
by the mechanical characteristics of the reinforcement in all practical cases, and
therefore not sensitive to εAAC max. One would also expect ductility and drift capacity
to be directly verifiable from wall tests. In subsequent chapters of this thesis,
those comparisons are made.
It is also necessary to examine the internal consistency of stress-strain data
reported here for low-strength AAC, with that reported by Tanner (2003). That
comparison is presented in Table 2.9, in terms of tested versus specified
compressive strengths and observed versus predicted values of EAAC. In that table,
the relationship between observed and specified compressive strength for low-
strength AAC is seen to be consistent with those for higher-strength AAC.
Additionally, the relationship between observed EAAC and that predicted by
Equation 2.1 is seen to be consistent with that reported previously for higher-
strength AAC. 6.06500 AACAAC fE = Equation 2.1
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R2 = 0.8002
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0 0.2 0.4 0.6 0.8 1 1.2 1.4f AAC (ksi)
e A
AC
max
Babb 3
Babb 2
Contec 1
Contec 2
Babb 1
Hebel 2
Ytong 2
Figure 2.22: Maximum useful strain versus compressive strength
Table 2.9: Material properties of this study versus those of Tanner (2003)
Study AACf
psi (MPa)
AACf '
psi (MPa)
AAC
AAC
ff'
Observed
EAAC
ksi (GPa)
Predicted
EAAC
ksi (GPa)
Observed /
Predicted
EAAC
This
study 344 (2.39) 290 (2.0) 1.18 223 (1.50) 195 (1.31) 1.14
Tanner
(2003) 715 (4.9) 580 (4.0) 1.23 296 (1.99) 295 (1.98) 1.00
Tanner
(2003) 1170 (8.0) 870 (6.0) 1.34 466 (3.13) 377 (2.54) 1.23
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2.3.6 Splitting Tensile Strength
Shear Wall Specimens 18 and 19 were constructed using AAC material
corresponding to Class PAAC2, which has a specified compressive strength of 2
MPa (290 psi). The tensile strength of the AAC material in those specimens was
tested.
2.3.6.1 Specimen Preparation and Testing Procedure for Splitting Tensile
Tests on AAC Masonry Units
Units for the splitting tensile tests were prepared from the AAC material
used to construct Shear Wall Specimens 18 and 19. This material had been
shipped to UT from Babb International, Inc. (Adel, GA). In this thesis, it is
designated as “Babb 3.”
Six units were prepared at UT for testing according to ASTM C1006. The
measurements of these units were 16137 in. (198 mm) high by 16
137 in. (198 mm)
wide by 24 in. (610 mm) long.
After the units were prepared, their weight, density and moisture contents
were measured. The moisture content of the units must be between 5 % and 15 %
according to ASTM C1386. The moisture content (MC) was measured three
times; at the time of the tensile test, at the end of the test, and five days after the
end of the test. Table 2.10 shows the moisture content recorded from the units.
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Table 2.10: Measured moisture contents (Babb 3 material)
Immediately before the Test Immediately after the Test 5 days after the Test
Unit Measured
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
Measured
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
Measured
Density
(pcf)
Dry
Density
(pcf)
MC
(%)
1 33.64 30.09 11.80 33.62 30.09 11.73 31.71 30.09 5.38
2 32.87 30.09 9.24 32.85 30.09 9.17 31.59 30.09 4.99
3 33.57 30.09 11.57 33.53 30.09 11.43 31.90 30.09 6.02
4 32.58 30.09 8.28 32.51 30.09 8.04 31.14 30.09 3.49
5 32.58 30.09 8.28 32.56 30.09 8.21 30.72 30.09 2.09
6 33.29 30.09 10.63 33.29 30.09 10.63 31.61 30.09 5.05
The test was performed in a universal machine, where the masonry units
were placed between two rods, one at the bottom face and the other at the top
face. Data were recorded using the readings of the universal machine. Figure 2.23
shows the test setup used in the splitting tensile tests.
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Figure 2.23: Test setup to measure splitting tensile strength
2.3.6.2 Splitting Tensile Strength for AAC Units
Splitting tensile strength for the six units, summarized in Table 2.11,
ranged from 49.02 psi (0.34 MPa) to 58.41 psi (0.40 MPa), with a mean of 52.85
psi (0.37 MPa) and a COV of 6.99 %.
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Table 2.11: Results of splitting tensile strength tests performed at UT Austin
Material Unit
Moisture
Content
(%)
Load
(Kips) tf
psi (MPa)
Average
psi (MPa)
COV
(%)
Average
psi (MPa)
COV
(%)
Babb 3 1 11.80 4.80 50.07 (0.35)
Babb 3 2 9.24 5.50 57.37 (0.40)
Babb 3 3 11.57 4.80 50.07 (0.35)
52.50
(0.36) 6.55
Babb 3 4 8.28 4.70 49.02 (0.34)
Babb 3 5 8.28 5.60 58.41 (0.40)
Babb 3 6 10.63 5.00 52.15 (0.36)
53.19
(0.37) 7.34
52.85 (0.37) 6.99
The results obtained for the tensile strength ranged from 16 % and 21 % of
the specified compressive strength of 290 psi (2 MPa), and from 14 % to 17 % of
the mean tested compressive strength of 344 psi (2.37 MPa).
2.3.6.3 Comparison between observed and predicted splitting tensile strength
of AAC
Through tensile strength tests performed at the University of Texas at
Austin and elsewhere, an equation (Equation 2.2) to predict the tensile strength of
AAC has been proposed (Argudo 2003).
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AACt ff '4.2=
Equation 2.2
The predicted tensile strength obtained using a specified compressive
strength of 290 psi (2 MPa) into Equation 2.2 was 40.87 psi (0.28 MPa). This
value corresponds to the 77% of the average tensile value obtained from the tests
which represents a conservative estimation of the real value. On the other hand,
after the evaluation of Equation 2.2 with the average compressive strength of 344
psi (2.37 MPa) obtained from the test a tensile strength of 44.51 psi (0.31 MPa)
was obtained which corresponds to 84.22 %, of the average tensile value. Figure
2.24 shows this last result (UT). Clearly, the relation between splitting tensile
strength and tested compressive strength for low-strength AAC, is consistent with
that obtained previously for higher-strength AAC.
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Babb 2(a)
Hebel 2Babb 1
Contec 2(b)Contec 1
Ytong 2
Ytong 1
Babb 2(b)
0
20
40
60
80
100
0 250 500 750 1000 1250 1500
Compressive strength (psi)
Split
ting
tens
ile s
tren
gth
(psi
)
0.0
0.1
0.3
0.4
0.5
0.70 1.7 3.4 5.1 6.8 8.5 10.2
Compressive strength (MPa)
Split
ting
tens
ile s
tren
gth
(MPa
)
UT300.05ff AACt +=
AACt f2.4f =
Babb 2(a)
Hebel 2Babb 1
Contec 2(b)Contec 1
Ytong 2
Ytong 1
Babb 2(b)
0
20
40
60
80
100
0 250 500 750 1000 1250 1500
Compressive strength (psi)
Split
ting
tens
ile s
tren
gth
(psi
)
0.0
0.1
0.3
0.4
0.5
0.70 1.7 3.4 5.1 6.8 8.5 10.2
Compressive strength (MPa)
Split
ting
tens
ile s
tren
gth
(MPa
)
UT Babb 2(a)
Hebel 2Babb 1
Contec 2(b)Contec 1
Ytong 2
Ytong 1
Babb 2(b)
0
20
40
60
80
100
0 250 500 750 1000 1250 1500
Compressive strength (psi)
Split
ting
tens
ile s
tren
gth
(psi
)
0.0
0.1
0.3
0.4
0.5
0.70 1.7 3.4 5.1 6.8 8.5 10.2
Compressive strength (MPa)
Split
ting
tens
ile s
tren
gth
(MPa
)
UT300.05ff AACt +=
AACt f2.4f =
Figure 2.24: Splitting tensile strength versus tested compressive strength
2.3.7 Construction of Shear Wall Specimens 18 and 19
The surface of the base beam was roughened and pre-wetted. A leveling
bed was applied, using conventional Portland cement-lime masonry mortar
conforming to ASTM C270, Type S by proportion. The masonry units were set up
in running bond and joined with thin-bed mortar. To prevent horizontal
misalignment, a guide string was connected to two guide poles located at each end
of the walls. The plumb was also checked every three courses during the
construction. Figure 2.25 shows construction details of Shear Wall Specimen 19.
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# 5 bars
Masonry UnitsGrout
# 5 bars
Masonry UnitsGrout
Figure 2.25: Plan view showing typical details of construction of Shear Wall
Specimen 19
Figure 2.26 and Figure 2.27 show the views of Shear Wall Specimens 18
and 19 respectively, after construction.
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Figure 2.26: Side view of Shear Wall Specimen 18
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Figure 2.27: Side view of Shear Wall Specimen 19
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CHAPTER 3 Test Results for AAC Shear Wall Specimens
3.1 INTRODUCTION
The objective of this chapter is to describe the results obtained from the
flexure-dominated wall (SWS17) and the shear-dominated walls (SWS18 and
SWS19). The results obtained for each specimen are accompanied by the
objectives, loading history, description of the major events observed during the
test, and hysteretic behavior of the walls. Design of each shear wall specimen
comprised the following steps: selection of plan length, which, in combination
with a constant specimen height, defined the specimen’s aspect ratio; selection of
the amount and distribution of flexural reinforcement, to encourage the desired
behavior; prediction of each limit state, based on that aspect ratio and flexural
reinforcement, using interaction diagrams of base shear capacity as a function of
axial load; and iteration of aspect ratio, flexural reinforcement and axial load to
produce a specimen with the intended behavior. When each specimen was tested,
its observed capacity in relevant limit states was compared with the corresponding
predicted capacity.
3.2 TEST RESULTS FOR SHEAR WALL SPECIMEN 17
The behavior of Shear Wall Specimen 17 is predicted using the interaction
diagram of Figure 3.1. In that interaction diagram, relevant behavior modes of the
specimen are represented, including flexural cracking, flexure-shear cracking,
sliding shear, web-shear cracking, and nominal flexural capacity. The applied
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axial load for Shear Wall Specimen 17 was selected as 25 kips (111.2 kN). At this
axial load, the major events in order of occurrence were flexural cracking,
flexure-shear cracking, and nominal flexural capacity. Web-shear cracking,
sliding shear, and crushing of the diagonal strut are not expected to occur because
the curves corresponding to them lie to the right of the curve representing nominal
flexural capacity.
0
25
50
75
100
0 20 40 60Shear Force (kips)
Axi
al F
orce
(kip
s)
0
111
222
334
4450 44 89 133 178
Shear Force (kN)
Axi
al F
orce
(kN
)
Web Shear Cracking
Flexural Capacity
Sliding Shear Failure
Crushing of Diag. Strut
Flexural Cracking
Flexural-Shear Cracking
Shear Wall Specimen 17
Figure 3.1: Prediction of behavior for Shear Wall Specimen 17
3.2.1 Loading History and Major Events for Shear Wall Specimen 17
The actual loading and displacement histories for Shear Wall Specimen 17
are presented in Figure 3.2 and Figure 3.3 respectively. The numbers on the
graphs refer to load points (each point during the test when data were recorded).
Positive values of the base shear force correspond to loading to the south, and
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negative values, to loading to the north. Each cycle is subdivided into an “a”
portion (positive displacements) followed by a “b” portion (negative
displacements). For each cycle of loading, the maximum loads and drift ratios are
shown in Table 3.1.
-40
-30
-20
-10
0
10
20
30
40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Load Point
Bas
e Sh
ear
(kip
s)
-178
-133
-89
-44
0
44
89
133
178
Bas
e Sh
ear
(kN
)
51 2 3 4 6 7 8 9 10 11 12
Figure 3.2: Actual loading history for Shear Wall Specimen 17
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-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Load Point
Dis
plac
emen
t (in
.)
-38
-25
-13
0
13
25
38
Dis
plac
emen
t (m
m)
3 954 621 7 8 10 11 12
Figure 3.3: Actual tip displacement history for Shear Wall Specimen17
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Table 3.1: Load Points, maximum load and drift ratios for each cycle for Shear
Wall Specimen 17
Cyc
le Load
Points
Max.
Applied
Load
(kips)
Max.
Applied
Load
(kN)
Max.
Drift
Ratio
(%)
Cyc
le Load
Points
Min.
Applied
Load
(kips)
Min.
Applied
Load
(kN)
Min.
Drift
Ratio
(%)
1a 1-60 5.71 25.42 0.010 1b 61-105 -8.29 -36.88 0.018
2a 106-141 6.95 30.92 0.012 2b 142-168 -7.92 -35.23 0.016
3a 169-204 11.41 50.80 0.027 3b 205-234 -13.01 -57.91 0.030
4a 235-259 12.32 54.83 0.030 4b 260-290 -13.25 -58.97 0.032
5a 291-334 18.56 82.57 0.062 5b 335-392 -19.70 -87.67 0.059
6a 393-437 18.87 83.95 0.067 6b 438-476 -19.88 -88.45 0.060
7a 477-530 25.31 112.63 0.134 7b 531-575 -24.34 -108.30 0.111
8a 576-622 26.03 115.83 0.156 8b 623-667 -27.86 -123.97 0.131
9a 668-727 30.01 133.53 0.344 9b 728-802 -32.99 -146.82 0.326
10a 803-884 32.73 145.63 0.653 10b 885-971 -33.46 -148.89 0.657
11a 972-1035 32.47 144.50 0.661 11b 1036-1103 -31.31 -139.33 0.649
12a 1104-1162 31.77 141.40 0.748
3.2.2 Sequence of Crack Formation for Shear Wall Specimen 17
The behavior of Shear Wall Specimen 17 is described through major
events observed during the test. These major events refer to significant changes in
the condition of the specimen. In Table 3.2, each major event is matched with its
respective load point and the corresponding changes in the specimen. In the
remainder of this section, each major event is discussed further.
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Table 3.2: Description of major events for Shear Wall Specimen 17
Major Event Load Point Physical Description
1 176 Flexural cracking, loading south
2 348 Flexural cracking, loading north
3 306 Propagation of flexural cracks, loading south
4 351 Propagation of flexural cracks, loading north
5 508 Flexure-shear crack, loading south
6 547 Flexure-shear crack, loading north
7 600-699 Propagation and additional flexure-shear cracks,
loading south
8 645-772 Propagation and additional flexure-shear cracks,
loading north
9 845, 854 Vertical crack formed between panels, loading
south
10 935 Vertical crack formed between panel and U-block,
loading north
11 940 Propagation of flexure-shear cracks, loading north
12 978 Propagation of flexure-shear cracks, loading south
13 1121 Crushing at north toe and fracture of the flexural
reinforcement at north end
3.2.2.1 Flexural Cracking in Shear Wall Specimen 17
According to Table 3.2, Major Events 1 and 2 correspond to flexural
cracking at the north end and the south ends of the specimen respectively. At the
north end of the specimen (loading to the south), flexural cracking occurred at a
load of 11.41 kips (50.8 kN) and a drift ratio of 0.026 % (Load Point 176). At the
south end of the specimen (loading to the north) flexural cracking occurred at a
load of 18.81 kips (83.72 kN) and a drift ratio of 0.053 % (Load Point 348).
Flexural cracking was predicted at a base shear of 12.1 kips (53.82 kN). The
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ratios of observed to predicted cracking strength were 0.94 (loading to the south)
and 1.55 (loading to the north).
As the test progressed, these flexural cracks propagated toward the center
of the specimen from both ends. These observations correspond to Major Events 3
and 4, which were recorded at Load Point 306 (loading to the south) and Load
Point 351 (loading to the north). This cracking pattern is shown in Figure 3.4.
N
Cracking inrecent events
N
Cracking inrecent events
Figure 3.4: Formation of flexural cracking in Shear Wall Specimen 17
3.2.2.2 Flexure-shear cracking in Shear Wall Specimen 17
Major Events 5 and 6 denote the formation of flexure-shear cracks while
loading south and north respectively. At the north end (loading to the south), these
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cracks formed at a base shear of 25.31 kips (112.63 kN) and a drift ratio of 0.13 %
(Load Point 508). This flexure-shear crack formed at the first and second U-
blocks at the bottom of Shear Wall Specimen 17, and continued to the middle of
the first panel at the north end of the specimen. These cracks are shown in detail
in Figure 3.5.
Figure 3.5: Flexure-shear cracks at north end of Shear Wall Specimen 17
At the south end (loading to the north), these cracks formed at a base shear
of 24.34 kips (108.30 kN) and a drift ratio of 0.082 % (Load Point 547). Flexural-
shear cracking was predicted at a base shear of 23.09 kips (102.70 kN). The ratios
of observed to predicted flexure-shear cracking strength were 1.09 (loading to the
south) and 1.05 (loading to the north).
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Yielding of the flexural reinforcement was observed at a base shear of
25.0 kips (111.2 kN) (loading to the south). This observation corresponds to
Major Event 7.
As the test progressed, existing flexure-shear cracks propagated at both
ends of the specimen. Additional flexure-shear cracks formed at approximately 12
in. (0.30m) and 24 in. (0.61m) from the bottom of the wall as the applied load
increased to 26.03 kips (115.83 kN) loading to the south, and to 27.86 kips
(123.97 kN) loading to the north. These observations also correspond to Major
Event 7 (Load Point 600) and Major Event 8 (Load Point 645). This cracking
pattern is shown in Figure 3.6.
N
Cracking in previous events
Cracking inrecent events
N
Cracking in previous events
Cracking inrecent events
Figure 3.6: Formation of flexural-shear cracks in Shear Wall Specimen 17
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3.2.2.3 Additional Cracking in Shear Wall Specimen 17
Major Events 9 and 10 correspond to the formation of additional flexure-
shear cracks and the development of vertical cracks in Shear Wall Specimen 17.
At the north end, additional flexure-shear cracks formed at Load Point 845, which
corresponded to a base shear of 32.11 kips (142.89 kN). These cracks were
located approximately 5 ft. (1.52m) from the base of the specimen, and
propagated from its north extreme fiber to the middle of the first panel. At Load
Point 935, similar crack propagation occurred at the south end, at a base shear of
33.28 kips (148.12 kN). Vertical cracks formed between the first and second
vertical panels at the north end of the specimen and between the fourth vertical
panel and the U-block at the south end of the specimen, approximately 6 ft.
(1.83m) from the bottom of the wall.
Major Events 11 and 12 correspond to propagation of previously formed
flexure-shear cracks. These observations correspond to Load Point 940 and Load
Point 978, loading to the north and south respectively. Figure 3.7 shows the
pattern of cracks at this stage of the test.
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N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.7: Formation of additional flexure-shear cracks, and propagation of
cracks from previous events
3.2.2.4 Final damage in Shear Wall Specimen 17
The final stage of testing of Shear Wall Specimen 17 was Major Event 13,
which denoted progressive damage at both ends of the specimen, as the
previously formed flexure-shear cracks propagated toward the center and the mid-
height of the wall. At Load Point 1121, which corresponded to a base shear of
17.81 kips (79.25 kN), toe spalling and crushing started at the north end. This
damage, along with yield of the flexural reinforcement, resulted in a gradual and
continuous drop in the in-plane lateral stiffness of the specimen. Capacity was
limited by fracture of flexural reinforcement at the north end of the specimen
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(while loading to the south), and was later confirmed as brittle fracture by the
absence of necking of the affected bar.
Figure 3.8 shows the damage in Shear Wall Specimen 17 at the end of the
test. The significant spalling at the bottom of the north end of the specimen during
the final increments of load is shown in Figure 3.9 and Figure 3.10.
N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.8: Cracking in Shear Wall Specimen 17 at end of test
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Figure 3.9: Spalling at the north end of Shear Wall Specimen 17
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Figure 3.10: Toe crushing north at north end of Shear Wall Specimen 17
3.2.3 Load-Displacement Behavior of Shear Wall Specimen 17
The overall hysteretic behavior of Shear Wall Specimen 17 is shown in
Figure 3.11. The initial stiffness of the load-displacement curve was 111 kip/in.
(16 kN/mm). Flexural reinforcement yielded at a base shear of 25 kips (111.2 kN)
and a corresponding displacement of 0.18 in. (0.45 mm). The test was stopped at a
tip displacement of 1 in. (25 mm) because the flexural reinforcement fractured at
the north end of the specimen.
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-40
-30
-20
-10
0
10
20
30
40
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
Drift Ratio (%)
Bas
e Sh
ear
(kip
s)
-178
-134
-89
-45
0
44
89
133
178
Bas
e Sh
ear
(KN
)
Figure 3.11: Overall hysteretic behavior of Shear Wall Specimen 17
3.3 TEST RESULTS FOR SHEAR WALL SPECIMEN 18
The behavior of Shear Wall Specimen 18 is predicted using the interaction
diagram of Figure 3.12. In that interaction diagram, relevant behavior modes of
the specimen are represented, including flexural cracking, sliding shear, web-
shear cracking, crushing of the diagonal strut and nominal flexural capacity. The
applied axial load for Shear Wall Specimen 18 was selected as 45 kips (200.5
kN). At this axial load, the major events in order of occurrence were flexural
cracking, web-shear cracking, crushing of diagonal strut, sliding shear failure,
flexure-shear cracking and yielding of flexural reinforcement. Sliding shear
cracking, flexure-shear cracking and yielding of flexural reinforcement were not
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expected to occur, because the curves corresponding to them lie to the right of the
curve representing web-shear cracking failure.
0
25
50
75
100
0 20 40 60 80 100Shear Force (kips)
Axi
al F
orce
(kip
s)
0
111
222
334
4450 89 178 267 356 445
Shear Force (kN)
Axi
al F
orce
(kN
)
Web Shear Cracking
Flexural Capacity
Sliding Shear Failure
Crushing of Diag. Strut
Flexural Shear Cracking
Flexural Cracking
Shear Wall Specimen 18
Figure 3.12: Prediction of behavior for Shear Wall Specimen 18
3.3.1 Loading History and Major Events for Shear Wall Specimen 18
The actual loading and displacement histories for Shear Wall Specimen 18
are presented in Figure 3.13 and Figure 3.14 respectively. The numbers on the
graphs refer to load points (each point during the test when data were recorded).
Positive values of the base shear force correspond to loading to the south, and
negative values, to loading to the north. Each cycle is subdivided into an “a”
portion (positive displacements) followed by a “b” portion (negative
displacements). The procedure of loading the specimen was started by loading
toward the south. For each cycle of loading, the maximum loads and drift ratios
are shown in Table 3.3.
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-50
-40
-30
-20
-10
0
10
20
30
40
50
0 150 300 450 600 750 900 1050 1200
Load Point
Bas
e Sh
ear
(kip
s)
-222
-178
-133
-89
-44
0
44
89
133
178
222
Bas
e Sh
ear
(kN
)
1 2 3 4 5 6 7 8 9 10
Figure 3.13: Actual loading history for Shear Wall Specimen 18
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-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0 200 400 600 800 1000 1200
Load Point
Disp
lace
men
t (in
.)
-25
-20
-15
-10
-5
0
5
10
15
20
25
Disp
lace
men
t (m
m)
1 2 3 4 5 6 7 8 9 10
Figure 3.14: Actual tip displacement history for Shear Wall Specimen 18
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Table 3.3: Load Points, maximum load drift ratios for each cycle for Shear
Wall Specimen 18
Cyc
le Load
Points
Max.
Applied
Load
(kips)
Max.
Applied
Load
(kN)
Max.
Drift
Ratio
(%)
Cyc
le Load
Points
Min.
Applied
Load
(kips)
Min.
Applied
Load
(kN)
Min.
Drift
Ratio
(%)
1a 1-56 9.30 41.38 0.020 1b 57-92 -9.45 -42.03 0.022
2a 93-149 9.53 42.43 0.020 2b 150-180 -10.16 -45.19 0.023
3a 181-245 18.77 83.51 0.048 3b 246-290 -19.31 -85.93 0.045
4a 291-348 20.31 90.39 0.056 4b 349-398 -20.36 -90.60 0.048
5a 399-475 27.87 124.04 0.102 5b 476-534 -28.09 -124.98 0.074
6a 535-599 28.32 126.02 0.107 6b 600-644 -28.29 -125.90 0.075
7a 645-726 38.59 171.71 0.186 7b 727-785 -38.63 -171.92 0.162
8a 786-858 39.01 173.62 0.200 8b 859-911 -37.99 -169.04 0.171
9a 912-987 43.61 194.06 0.343 9b 988-1052 -42.46 -188.96 0.392
10a 1053-1136 33.17 147.59 0.477 10b 1137-1188 -23.81 -105.97 0.482
3.3.2 Sequence of Crack Formation for Shear Wall Specimen 18
The behavior of Shear Wall Specimen 18 is described through major
events observed during the test. These major events refer to significant changes in
the condition of the specimen. Each major event is matched with its respective
load point and the corresponding changes in the specimen, in Table 3.4. In the
remainder of this section, each major event is discussed further.
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Table 3.4: Description of major events for Shear Wall Specimen 18
Major Event Load Point Physical Description
1 441 Flexural cracking, loading south
2 509 Flexural cracking, loading north
3 456 Propagation of flexural cracks, loading south
4 517 Propagation of flexural cracks, loading north
5 689 Web-shear cracking, loading south
6 754, 763 Web-shear cracking, loading north
7 696, 829 Additional Web-shear cracking, loading south
8 763, 889 Additional Web-shear cracking, loading north
9 952, 961 Diagonal cracks formed, loading south
10 1001, 1023 Diagonal cracks formed, loading north
11 1034 Additional diagonal cracks formed with toe
crushing, loading north
12 1089, 1103 Additional diagonal cracks formed with toe
crushing, loading south
3.3.2.1 Flexural cracking in Shear Wall Specimen 18
According to Table 3.4, Major Events 1 and 2 correspond to flexural
cracking at the north and south ends of the specimen respectively. At the north
end of the specimen (loading to the south), flexural cracking occurred at a load of
22.63 kips (100.69 kN) and a drift ratio of 0.068 % (Load Point 441). At the south
end of the specimen (loading to the north) flexural cracking occurred at a load of
24.99 kips (111.23 kN) and a drift ratio of 0.062 % (Load Point 509). Flexural
cracking was predicted at a base shear of 19.0 kips (84.51 kN). The ratios of
observed to predicted cracking strength were 1.19 (loading to the south) and 1.32
(loading to the north).
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As the test progressed, these flexural cracks propagated toward the center
of the specimen from both ends. These observations correspond to Major Events 3
and 4, which were recorded at Load Point 456 (loading to the south) and Load
Point 517 (loading to the north). This cracking pattern is shown in Figure 3.15.
N
Cracking in recent events
N
Cracking in recent events
Figure 3.15: Formation of flexural cracking in Shear Wall Specimen 18
3.3.2.2 Web-shear cracking in Shear Wall Specimen 18
Major Events 5 and 6 denote the formation of web-shear cracking while
loading south and north respectively. At the north end (loading to the south), these
cracks formed at a base shear of 36.07 kips (160.50 kN) and a drift ratio of 0.16 %
(Load Point 689). This web-shear crack formed at the third and fifth course of
blocks approximately 24 in. (0.61 m) and 40 in. (1.02 m) from the bottom of
Shear Wall Specimen 18. These cracks are shown in detail in Figure 3.16.
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Figure 3.16: Web-shear cracking at north end of Shear Wall Specimen 18
At the south end (loading to the north), these cracks formed at a base shear
of 35.66 kips (158.70 kN) and a drift ratio of 0.120 % (Load Point 754). Web-
shear cracking was predicted at a base shear of 37.0 kips (164.58 kN). The ratios
of observed to predicted web-shear cracking strength were 0.97 (loading to the
south) and 0.96 (loading to the north).
As the test progressed, existing web-shear cracks propagated at both ends
of the specimen. Additional web-shear cracks formed in the fifth course of units,
approximately 40 in. (1.02 m) from the bottom of the wall as the applied load
increased to 38.59 kips (171.71 kN), loading to the south and 38.63 kips (171.92
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kN), loading to the north. These observations correspond to Major Event 7 (Load
Point 696) and Major Event 8 (Load Point 763). The corresponding cracking
pattern is shown in Figure 3.17.
N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.17: Web-shear cracking in Shear Wall Specimen 18
3.3.2.3 Propagation and Additional Web-shear cracking in Shear Wall
Specimen 18
Major Events 9 and 10 correspond to the propagation of existing web-
shear cracks and the development of new web-shear cracks in Shear Wall
Specimen 18. At the north end, additional web-shear cracks formed at Load Point
952 which corresponded to a base shear force of 40.69 kips (181.07 kN). These
cracks were located along the height of the wall and spread from the north end of
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the wall toward the center of it. At Load Point 1023, similar cracks occurred at the
south end, at a base shear of 42.46 kips (188.96 kN). Diagonal cracks formed
close to the south end of the wall. At this stage of the test, the north end of the
specimen showed a major level of damage, with a large amount of cracking
developing toward the center of the wall. This cracking pattern showed that the
specimen was close to toe crushing. The cracking pattern associated with Major
Events 9 and 10 is shown in Figure 3.18.
N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.18: Propagation and formation of additional web-shear cracks in
Shear Wall Specimen 18
3.3.2.4 Final damage in Shear Wall Specimen 18
Major Events 11 and 12 denoted the final stage in the test of Shear Wall
Specimen 18, and were associated with progressive damage at both ends of the
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specimen. This damage consisted of the propagation and formation of additional
web-shear cracks extended through the units and the mortar joints. At Load Point
1034, corresponding to a base shear of 35.03 kips (155.87 kN), toe crushing was
observed at the south end of the specimen. An analogous situation occurred at the
north end at Load Point 1089, which corresponded to a base shear of 34.73 kips
(154.54 kN). At this stage, the specimen showed toe crushing at both ends, and
significant reductions in in-plane stiffness (about 21 % of the initial stiffness) and
shear capacity. This observation is base on the reduction in slope showed by the
hysteretic curve. The test was ended in Loading Cycle 10, at a maximum base
shear of 31.82 kips (141.59 kN).
Figure 3.19 shows the damage in Shear Wall Specimen 18 at the end of
the test. The significant extent and width of web-shear cracks are shown in Figure
3.20 and Figure 3.21.
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N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.19: Additional web-shear cracking and toe crushing in Shear Wall
Specimen 18
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Figure 3.20: Web-shear cracks in Shear Wall Specimen 18
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Figure 3.21: Toe crushing at the north end of Shear Wall Specimen 18
3.3.3 Load-Displacement Behavior for Shear Wall Specimen 18
The overall hysteretic behavior of Shear Wall Specimen 18 is shown in
Figure 3.22. The maximum drift ratio for this specimen was about 0.48 % in both
directions. The test was stopped at in-plane displacements of 0.73 in. (18.54 mm).
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-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Drift Ratio (%)
Bas
e Sh
ear
(kip
s)
-222
-178
-133
-89
-44
0
44
89
133
178
222
Bas
e Sh
ear
(kN
)
Figure 3.22: Overall hysteretic behavior of Shear Wall Specimen 18
3.4 SHEAR WALL SPECIMEN 19
The behavior of Shear Wall Specimen 19 was predicted using the
interaction diagram of Figure 3.23. In that interaction diagram, relevant behavior
modes of the specimen are represented, including flexural cracking, sliding shear,
web-shear cracking, crushing of the diagonal strut and nominal flexural capacity.
The applied axial load for Shear Wall Specimen 19 was selected as 58 kips (258.0
kN). At this axial load, the major events in order of occurrence were flexural
cracking, web-shear cracking, crushing of diagonal strut, sliding shear failure, and
yielding of flexural reinforcement. Sliding shear cracking and yielding of flexural
reinforcement are not expected to occur because the curves corresponding to them
lie to the right of the curve representing web-shear cracking failure.
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0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100
Base Shear (kips)
Axi
al F
orce
(kip
s)
0
111
222
334
4450 89 178 267 356 445
Base Shear (kN)
Axi
al F
orce
(kN
)
Web Shear Cracking
Sliding Shear Failure
Crushing of Diag. Strut
Yielding of flexuralreinforcement
Flexural Cracking
Shear Wall Specimen 19
Figure 3.23: Prediction of behavior for Shear Wall Specimen 19
3.4.1 Loading History and Major Events for Shear Wall Specimen 19
The actual loading and displacement histories for Shear Wall Specimen 19
are presented in Figure 3.24 and Figure 3.25 respectively. The numbers on the
graphs refer to load points (each point during the test when data were recorded).
Positive values of the base shear force correspond to loading to the south, and
negative values, to loading to the north. Each cycle is subdivided into an “a”
portion (positive displacements) followed by a “b” portion (negative
displacements). The procedure of loading the specimen was started by loading
toward the south. For each cycle of loading, the maximum loads and drift ratios
are shown in Table 3.5.
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80
-80
-60
-40
-20
0
20
40
60
80
0 150 300 450 600 750 900 1050 1200
Load Point
Bas
e Sh
ear
(kip
s)
-356
-267
-178
-89
0
89
178
267
356
Bas
e Sh
ear
(kN
)
1 2 3 4 5 6 7 8 9 10
Figure 3.24: Actual loading history for Shear Wall Specimen 19
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-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0 200 400 600 800 1000 1200 1400
Load Point
Dis
plac
emen
t (in
.)
-20
-15
-10
-5
0
5
10
15
20
Dis
plac
emen
t (m
m)
1 2 3 4 5 6 7 8 9 10
Figure 3.25: Actual tip displacement history for Shear Wall Specimen 19
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Table 3.5: Load Points, maximum load and drift ratios for each cycle for Shear
Wall Specimen 19
Cyc
le Load
Points
Max.
Applied
Load
(kips)
Max.
Applied
Load
(kN)
Max.
Drift
Ratio
(%)
Cyc
le Load
Points
Min.
Applied
Load
(kips)
Min.
Applied
Load
(kN)
Min.
Drift
Ratio
(%)
1a 1-81 22.26 99.04 0.027 1b 82-148 -21.94 -97.62 0.026
2a 149-206 21.95 97.67 0.026 2b 207-255 -22.11 -98.37 0.026
3a 256-338 44.72 198.99 0.079 3b 339-400 -46.41 -206.53 0.063
4a 401-453 46.02 204.79 0.086 4b 454-500 -46.35 -206.26 0.063
5a 501-550 50.21 223.44 0.100 5b 551-602 -50.00 -222.50 0.070
6a 603-672 50.48 224.66 0.103 6b 673-717 -51.09 -227.37 0.074
7a 718-800 56.00 249.21 0.142 7b 801-857 -61.38 -273.12 0.118
8a 858-915 56.78 252.66 0.174 8b 916-979 -59.55 -265.00 0.130
9a 980-1037 62.21 276.85 0.263 9b 1038-1100 -65.02 -289.33 0.290
10a 1101-1163 51.58 229.52 0.449 10b 1164-1234 -41.52 -184.78 0.464
3.4.2 Sequence of Crack Formation for Shear Wall Specimen 19
The behavior of Shear Wall Specimen 19 is described through major
events observed during the test. These major events refer to significant changes in
the condition of the specimen. Each major event is matched with its respective
load point and the corresponding changes in the specimen, in Table 3.6. In the
remainder of this section, each major event is discussed further.
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Table 3.6: Description of major events for Shear Wall Specimen 19
Major Event Load Point Physical Description
1 304 Flexural cracking, loading south
2 357 Flexural cracking, loading north
3 317 Propagation of flexural cracks, loading south
4 376 Propagation of flexural cracks, loading north
5 751 Web-shear cracking, loading south
6 828,833 Web-shear cracking, loading north
7 884 Flexure-shear cracks, loading south
8 890 Additional Web-shear cracking, loading south
9 955 Additional Web-shear cracking and flexure-shear
cracking, loading north
10 1016 Diagonal cracks formed, loading south
11 1073 Diagonal cracks formed, loading north
12 1083 Additional diagonal cracks formed with toe
crushing, loading north
13 1134 Additional diagonal cracks formed with toe
crushing, loading south
3.4.2.1 Flexural cracking in Shear Wall Specimen 19
According to Table 3.6, Major Events 1 and 2 correspond to flexural
cracking at the north end and the south end of the specimen respectively. At the
north end of the specimen (loading to the south), flexural cracking occurred at a
load of 39.06 kips (173.82 kN) and a drift ratio of 0.062 % (Load Point 304). At
the south end of the specimen (loading to the north) flexural cracking occurred at
a load of 25.07 kips (111.58 kN) and a drift ratio of 0.028 % (Load Point 357).
Flexural cracking was predicted at a base shear of 43.0 kips (191.26 kN). The
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ratios of observed to predicted cracking strength were 0.91 (loading to the south)
and 0.58 (loading to the north).
As the test progressed, these flexural cracks propagated toward the center
of the specimen from both ends. These observations correspond to Major Events 3
and 4, which were recorded at Load Point 317 (loading to the south) and Load
Point 376 (loading to the north). This cracking pattern is shown in Figure 3.26.
N
Cracking in recent events
N
Cracking in recent events
Figure 3.26: Flexural cracks in Shear Wall Specimen 19
3.4.2.2 Web-shear cracking in Shear Wall Specimen 19
Major Events 5 and 6 denote the formation of web-shear cracking while
loading south and north respectively. At the north end (loading to the south), these
cracks formed at a base shear of 56.00 kips (249.21 kN) and a drift ratio of 0.126
% (Load Point 751). This web-shear crack formed approximately in the central
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portion of the specimen and covered Shear Wall Specimen 19 from top to bottom.
These cracks are shown in detail in Figure 3.27.
Figure 3.27: Web-shear cracking in Shear Wall Specimen 19
At the south end (loading to the north), these cracks formed at a base shear
force of 54.84 kips (244.04 kN) and a drift ratio of 0.083 % (Load Point 828).
Web-shear cracking was predicted at a base shear of 52.0 kips (231.30 kN). The
ratios of observed to predicted web-shear cracking strength were 1.07 (loading to
the south) and 1.05 (loading to the north).
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As the test progressed, flexure-shear cracking was observed at Load Point
884, which corresponded to Major Event 7. This cracking was located at the north
end of the specimen, approximately 30 in. (0.76 m) from the bottom of Shear
Wall Specimen 19. Major Event 8, which corresponded to Load Point 890 and a
base shear force of 56.78 kips (252.66 kN), was characterized by the propagation
of the existing web-shear cracks from the middle height of the specimen toward
the bottom of the specimen. Major Event 9 is characterized by the formation of
additional flexure-shear cracks and the propagation of those cracks toward the
bottom of the specimen. This was observed as the applied load was 59.55 kips
(265.00 kN), loading to the north. Cracking associated with Major Events 7, 8 and
9 is shown in Figure 3.28.
N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.28: Web-shear cracking in Shear Wall Specimen 19
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3.4.2.3 Propagation and Additional Web-shear cracking in Shear Wall
Specimen 19
Major Events 10 and 11 correspond to the propagation of existing web-
shear cracks and the development of new web-shear cracks in Shear Wall
Specimen 19. At the north end, additional web-shear cracks formed at Load Point
1016, which corresponded to a base shear of 62.21 kips (276.85 kN). These
cracks were extended through the wall and covering the center portion of the
specimen almost to the base of the south end. A similar situation was observed at
the south end of Shear Wall Specimen 19, specifically at Load Point 1073,
corresponding to a base shear of 65.02 kips (289.33 kN). These diagonal cracks
formed from the top to the bottom of the specimen and extended from the center
portion of the specimen toward its north base. At this stage of the test, the south
end of the specimen showed major damage, with cracking developing from the
mid-height of the south end toward the bottom of it. The cracking pattern
associated with Major Events 10 and 11 is shown in Figure 3.29.
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N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.29: Propagation and formation of additional web-shear cracks along
with some flexure-shear cracks in Shear Wall Specimen 19
3.4.2.4 Final damage in Shear Wall Specimen 19
Major Events 12 and 13 denote the final stage in the test of Shear Wall
Specimen 19, and are associated with progressive damage at both ends of the
specimen. This damage consisted of the propagation and formation of additional
web-shear cracks in the specimen from the top to the bottom. At Load Point 1083,
which corresponded to a base shear of 64.83 kips (288.47 kN), toe crushing was
observed at the north end of the specimen. A similar situation occurred at the
south end of the specimen at Load Point 1134, which corresponded to a base
shear of 51.58 kips (229.52 kN). At this stage, the specimen showed major
damage with crushing of both compressive toes, along with a significant drop in
in-plane stiffness (about 14 % of the initial stiffness) and strength. This
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observation is based on the reduction in slope of the hysteretic curve. The test was
ended in Loading Cycle 10.
Figure 3.30 shows the damage in Shear Wall Specimen 19 at the end of
the test. The significant amount and opening of the web-shear cracks and crushing
of the diagonal strut is shown in Figure 3.31 and Figure 3.32 respectively.
N
Cracking in previous events
Cracking in recent events
N
Cracking in previous events
Cracking in recent events
Figure 3.30: Additional web-shear cracking and toe crushing in Shear Wall
Specimen 19
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Figure 3.31: Web-shear cracking in Shear Wall Specimen 19 at the end of the
test
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Figure 3.32: Toe crushing at the north end of Shear Wall Specimen 19
3.4.3 Load-Displacement Behavior for Shear Wall Specimen 19
The overall hysteretic behavior of Shear Wall Specimen 19 is shown in
Figure 3.33. The maximum drift ratio for this specimen was about 0.49 % in both
directions. The test was stopped at in-plane displacements of 0.71 in (18.00 mm).
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-80
-60
-40
-20
0
20
40
60
80
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Drift Ratio (%)
Bas
e S
hear
(Kip
s)
-356
-267
-178
-89
0
89
178
267
356
Bas
e Sh
ear
(kN
)
Figure 3.33: Overall hysteretic behavior of Shear Wall Specimen 19
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CHAPTER 4 Significance of Test Results
In this chapter, the overall hysteretic behavior of each specimen is
evaluated and compared with predicted behavior. Each observed behavior mode
is confirmed, and the validity of previously proposed design provisions is
assessed for flexure- as well as shear-dominated behavior.
4.1 REVIEW OF BEHAVIOR MODES FOR AAC SHEAR WALLS
For the specimens tested at UT, the relevant design-related behavior
modes are: flexural cracking, web-shear cracking, flexure-shear cracking, yielding
of the flexural reinforcement, crushing of the diagonal strut, and sliding shear. In
this section, the previously developed design provisions for each behavior mode
are reviewed (Tanner 2003, Argudo 2003). In subsequent sections, the capacities
predicted by those design provisions are compared with the observed capacities
for each specimen.
4.1.1 Flexural Cracking
Flexural cracking occurs when the flexural tensile strength of the material,
which is represented by the modulus of rupture, is exceeded by the flexural tensile
stress. For design purposes, the modulus of rupture is given by Equation 4.1 , and
is capped at 50 psi (0.34 MPa). The general form of the proposed equation for
flexural cracking is based on principal tensile stresses (Equation 4.2) (Tanner
2003 and Appendix A of this thesis). Flexural cracking occurs at the base of a
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cantilever wall because the moment is greatest there (Figure 4.1). If the element
has flexural reinforcement, flexural cracking does not constitute failure.
AACr ff 4.22×= Equation 4.1
+×=
w
ur
wcr tl
NfhtlV6
2
Equation 4.2
N
V
FlexuralCracking
N
V
FlexuralCracking
Figure 4.1: Typical flexural cracking
Shear Wall Specimens 17, 18 and 19 exhibited flexural cracking. Table
4.1 shows the ratios of observed to predicted flexural cracking capacities for these
specimens (SWS17, SWS18, and SWS19) and the corresponding mean value for
the specimens tested at The University of Texas at Austin by Tanner (2003).
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Table 4.1 Observed versus predicted flexural cracking capacities
Specimen
Number
Observed
Base Shear
Capacity, kips
(kN)
Predicted
Base Shear
Capacity
kips (kN)
Observed /
Predicted Capacity
17 15.11 (67.2) 12.10 (53.82) 1.25 18 23.81 (105.9) 19.00 (84.51) 1.25 19 32.07 (142.6) 43.00 (191.26) 0.75
Specimens of
Tanner (2003)
27.83 (123.8)
COV (99 %)
25.11 (111.70)
COV (95 %)1.10
Table 4.1 shows a good agreement between the observed and predicted
flexural cracking capacities of the three specimens tested in this study, and good
consistency between the specimens of this study and those reported by Tanner
(2003).
4.1.2 Web-shear cracking
Web-shear cracking occurs when principal tensile stresses exceed the
diagonal tensile strength of the AAC material (Figure 4.2). This type of cracking
was observed in Shear Wall Specimens 17 and 18.
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N
V
Web-shearCracking
N
V
Web-shearCracking
Figure 4.2: Typical web-shear cracking
The design equation for web-shear cracking capacity of fully mortared
AAC shear walls is given in Equation 4.3 (Tanner 2003 and Appendix A of this
thesis).
tlfNftlV
wAAC
uAACwAAC '4.2
1'9.0 += Equation 4.3
Shear Wall Specimens 18 and 19 exhibited web-shear cracking. Table 4.2
shows observed versus predicted web-shear cracking capacities for these
specimens, along with the corresponding mean value for the specimens tested at
The University of Texas at Austin by Tanner (2003). The table shows good
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97
agreement between the observed and predicted web-shear cracking capacities of
the shear-dominated specimens tested in this study, and reasonable consistency
between the specimens of this study and those reported by Tanner (2003).
Table 4.2 Observed versus predicted web-shear cracking capacities
Specimen
Number
Observed
Base Shear
Capacity, kips
(kN)
Predicted
Base Shear
Capacity, kips
(kN)
Observed /
Predicted Capacity
18 35.87 (159.5) 37.0 (164.5) 0.97 19 55.42 (246.5) 52.0 (231.3) 1.06
Specimens of
Tanner (2003) 72.3 (321.5)
COV (64 %)
58.0 (257.5)
COV (58 %) 1.24
4.1.3 Flexure-shear cracking
Flexure-shear cracking occurs when principal tensile stresses are sufficient
to cause a flexural crack to propagate diagonally into the web of the element
(Figure 4.3).
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V
Flexure-shearCracking
V
Flexure-shearCracking
Figure 4.3: Typical flexure-shear cracking
The design formula used for flexure-shear cracking capacity is given in
Equation 4.4, and includes the previously developed expression for the diagonal
tensile strength of AAC material as discussed in Chapter 2 of this thesis (Tanner
2003, Argudo 2003).
tdlVM
tlNfl
fVw
wAACw
AACc
−
+
+=
2
21.0'25.1'6.0
Equation 4.4
As discussed in Tanner (2003) and in Appendix A of this thesis, flexure-
shear cracking does not constitute a limit state in the specimens tested at the
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University of Texas at Austin, because it is not associated with a significant
change in capacity or stiffness.
Shear Wall Specimen 17 exhibited flexure-shear cracking. Table 4.3
shows the results of observed versus predicted flexure-shear cracking capacity for
this specimen and the corresponding mean value for the specimens tested at The
University of Texas at Austin by Tanner (2003). The values for SWS 17 are
consistent with values reported by Tanner.
Table 4.3 Observed versus predicted flexure-shear cracking capacities
Specimen
Number
Observed
Base Shear
Capacity,
kips (kN)
Predicted
Base Shear
Capacity, kips
(kN)
Observed / Predicted
Capacity
17 24.83 (110.4) 23.09 (102.7) 1.08 Specimens of
Tanner (2003)
13.63 (60.6)
COV (66 %)
12.24 (54.44)
COV (63 %) 1.11
4.1.4 Nominal Flexural Capacity
The nominal flexural capacity of the flexure-dominated AAC shear-wall
specimens tested at The University of Texas at Austin was determined using
conventional flexural theory (Figure 4.4), using a maximum compressive strain in
the AAC material of 0.003, and an equivalent rectangular stress block with a
height of 0.85f'AAC and a depth 67.01 =β (Argudo 2003). The design formula
used for nominal flexural capacity is given in Equation 4.5.
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100
Plan View of the wall Strain Distribution
Cs = As*f’s
Cc = 0.85f’AAC(β1c)c β1c
Force Distribution
Reinforcement0.85f’AAC
Plan View of the wall Strain Distribution
T=As*fs
c β1c
Force Distribution
0.85f’AAC
εs
ε'sεAAC max
Plan View of the wall Strain Distribution
Cs = As*f’s
Cc = 0.85f’AAC(β1c)c β1c
Force Distribution
Reinforcement0.85f’AAC
Plan View of the wall Strain Distribution
T=As*fs
c β1c
Force Distribution
0.85f’AAC
εs
ε'sεAAC max
Figure 4.4: Strain and force distribution in an AAC shear wall
−×= iwss
n xlhfAV
2
Equation 4.5
Because the behavior of Shear Wall Specimens 18 and 19 was governed
(as intended) by web-shear cracking rather than flexure, they did not reach their
nominal flexural capacity. Shear Wall Specimen 17, whose behavior was
governed (as intended) by flexure, did reach its nominal flexural capacity. Table
4.4 shows that the ratios of observed versus predicted nominal flexural capacities
for this specimen are very consistent with the corresponding mean flexural
capacities of the specimens tested at The University of Texas at Austin (Tanner
2003). Although εAAC max decreases below 0.003 for low-strength AAC, nominal
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101
flexural capacities are still well predicted, because they are governed by the
reinforcement.
Table 4.4 Observed versus predicted values for nominal flexural capacity
Specimen
Number
Observed
Base Shear
Capacity,
kips (kN)
Predicted
Base Shear
Capacity, kips
(kN)
Observed / Predicted
Capacity
17 25.0 (111.2) 25.8 (114.8) 0.97 Specimens
Tanner (2003)
19.4 (86.2)
COV (58 %)
18.65 (83.0)
COV (54 %)
1.04
COV (6 %)
4.1.5 Crushing of the Diagonal Strut
Crushing of the diagonal strut occurs when high overturning moments and
high base shears combine to produce a localized compression failure at the toe of
an AAC shear wall (Figure 4.5).
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102
N
V
Diagonal Crack Crushing of the AAC
N
V
Diagonal Crack Crushing of the AAC
Figure 4.5: Diagonal cracks and crushing of the diagonal strut
The design provisions previously proposed by Tanner (2003) for crushing
of the diagonal strut are based on the results of tests conducted at The University
of Texas at Austin (Tanner 2003, Varela 2003). In that development, a horizontal
width of the diagonal strut of wl25.0 was used. The equation (Equation 4.6) must
be checked only for walls with M/Vd < 1.5, because this failure mode does not
occur for walls with M/Vd ≥ 1.5 (Tanner 2003).
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103
+
×= 22
2
43
'17.0
w
wAACAAC
lh
hltfV Equation 4.6
Shear Wall Specimens 18 and 19 exhibited crushing of the diagonal strut.
Table 4.5 shows ratios of observed versus predicted capacities as governed by
crushing of the diagonal strut for these specimens, and the corresponding mean
value of those ratios for the specimens tested at The University of Texas at Austin
by Tanner (2003).
Table 4.5 Observed versus predicted capacities as governed by crushing of the
diagonal strut
Specimen
Number
Observed
Base Shear
Capacity,
kips (kN)
Predicted
Base Shear
Capacity, kips
(kN)
Observed / Predicted
Capacity
18 34.88 (155.15) 39.26 (174.63) 0.89 19 58.21 (258.92) 62.56 (278.27) 0.93
Specimens
Tanner (2003)
108.5 (482.6)
COV (73 %)
120.5 (536.0))
COV (73 %) 0.90
Table 4.5 shows a good agreement of ratios between the observed and
predicted crushing of the diagonal strut for the shear-dominated specimens tested
in this study, and good consistency between the specimens of this study and those
reported by Tanner (2003).
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104
4.1.6 Sliding Shear
Sliding shear occurs along a bed joint when the shear there exceeds the
combined capacity from adhesion and shear friction (Figure 4.6, Figure 4.7).
N
Sliding-shearCracking
V
N
Sliding-shearCracking
V
Figure 4.6 Sliding-shear cracking
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105
dowel action
Reinforcement
Shear slip failure
N
N
V
V
dowel action
Reinforcement
Shear slip failure
N
N
V
V
Figure 4.7: Shear friction
As previously developed by Tanner (2003), sliding-shear capacity is given
by Equation 4.7.
svfsliding fANV += Equation 4.7
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106
For design purposes, the contribution of reinforcement is conservatively
neglected (Tanner 2003), leading to Equation 4.8. Because sliding shear was not
observed in Shear Wall Specimens 17, 18 and 19, comparison with the results of
Tanner is not possible.
usliding NV µ=
Equation 4.8
4.2 HYSTERETIC BEHAVIOR OF SHEAR WALL SPECIMENS
In this section, the hysteretic behavior of Shear Wall Specimens 17, 18
and 19 is presented and compared with that obtained in the specimens tested by
Tanner (2003) and Varela (2003). The behavior of the flexure-dominated
specimen (SWS17) is described first, followed by the behavior of the shear-
dominated specimens (SWS 18 and SWS 19).
4.2.1 Hysteretic Behavior of Flexure-Dominated Specimens
The hysteretic load-displacement response of flexure-dominated AAC
shear-wall specimens can be described in terms of the following:
• initial stiffness;
• stiffness after flexural cracking;
• stiffness after yielding of the flexural reinforcement;
• unloading stiffness after yielding of the flexural reinforcement;
• capacity;
• degradation of stiffness with cycling;
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107
• degradation of strength with cycling; and
• displacement ductility.
For flexure-dominated Shear Wall Specimen 17, initial tangent stiffness
(Kot-o) was calculated as the slope of the first half-cycle of the load-displacement
curve. The initial backbone stiffness (Kob-o) was calculated as the slope of the
straight line between the origin and the last point in that first half-cycle (Figure
4.8).
-50
-40
-30
-20
-10
0
10
20
30
40
50
-1.5 -1 -0.5 0 0.5 1 1.5Displacement (in.)
Bas
e Sh
ear (
kips
)
-225
-180
-135
-90
-45
0
45
90
135
180
225-38.1 -25.4 -12.7 0 12.7 25.4 38.1
Displacement (mm)
Bas
e Sh
ear (
kN)
Kot-o
Initial Tangent Stiffness
Kob-o
Initial Backbone Stiffness
Figure 4.8: Initial tangent and backbone stiffness for Shear Wall Specimen 17
The secant stiffness after flexural cracking was calculated as the applied
load at which yielding of the flexural reinforcement was observed, divided by the
corresponding horizontal displacement (Figure 4.9). Yielding of the flexural
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108
reinforcement was detected using strain gages on the flexural reinforcement. Dys
and Dyn are the displacements at yielding of the flexural reinforcement in the
south and north directions respectively, and Kcr-os and Kcr-on are the corresponding
stiffnesses.
-50
-40
-30
-20
-10
0
10
20
30
40
50
-1.5 -1 -0.5 0 0.5 1 1.5Displacement (in.)
Bas
e Sh
ear (
kips
)
-225
-180
-135
-90
-45
0
45
90
135
180
225-38.1 -25.4 -12.7 0 12.7 25.4 38.1
Displacement (mm)
Bas
e Sh
ear (
kN)
Kcr-os
Kcr-on
Stiffness AfterFlexural Cracking North
Stiffness AfterFlexural Cracking South
Yielding of the FlexuralReinforcement South
Yielding of the FlexuralReinforcement North
Figure 4.9: Stiffness after flexural cracking for Shear Wall Specimen 17
The unloading stiffness after yielding of the flexural reinforcement was
calculated using the tangent to the load-displacement curve on first unloading
after observed yield of flexural reinforcement (Figure 4.10). Two unloading
stiffnesses were calculated for the specimen, one corresponding to displacements
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109
in the south direction (Ku-os) and the other to displacements in the north direction
(Ku-on).
-50
-40
-30
-20
-10
0
10
20
30
40
50
-1.5 -1 -0.5 0 0.5 1 1.5Displacement (in.)
Bas
e Sh
ear (
kips
)
-225
-180
-135
-90
-45
0
45
90
135
180
225-38.1 -25.4 -12.7 0 12.7 25.4 38.1
Displacement (mm)
Bas
e Sh
ear (
kN)
Ku-os
Ku-on
Unloading Stiffness AfterYielding of the Flexural Reinforcement South
Yielding of the FlexuralReinforcement South
Yielding of the FlexuralReinforcement North
Unloading Stiffness AfterYielding of the Flexural Reinforcement North
Figure 4.10: Unloading stiffnesses after yielding of the flexural reinforcement
for Shear Wall Specimen 17
The stiffness after yielding of the flexural reinforcement was calculated as
the slope of the tangent to the load-displacement curve after observed yield of
flexural reinforcement (Figure 4.11). Two stiffnesses after yielding of the flexural
reinforcement were calculated for this flexure-dominated specimen, one
corresponding to loading the specimen in the south direction (Ky-os), and the other
in the north direction (Ky-on).
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110
-50
-40
-30
-20
-10
0
10
20
30
40
50
-1.5 -1 -0.5 0 0.5 1 1.5Displacement (in.)
Bas
e Sh
ear (
kips
)
-225
-180
-135
-90
-45
0
45
90
135
180
225-38.1 -25.4 -12.7 0 12.7 25.4 38.1
Displacement (mm)
Bas
e Sh
ear (
kN)
(Ky-os)
Stiffness After Yielding of theFlexural Reinforcement South
Stiffness After Yielding of theFlexural Reinforcement North
(Ky-on)
Figure 4.11: Stiffnesses after yielding of the flexural reinforcement for Shear
Wall Specimen 17
The maximum useful horizontal displacement was taken as that
corresponding to the smaller of the following displacements:
• the displacement corresponding to a reduction of more than 10 % in the
maximum capacity of the specimen in a given load cycle, compared to the
maximum capacity in the same direction in the previous load cycle; and
• the displacement corresponding to a significant change in the shape of the
hysteretic loop from the corresponding previous load cycle.
Using this maximum useful displacement, maximum global drift ratios were
calculated for this flexure-dominated specimen, one corresponding to loading the
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111
specimen in the south direction (δos) and the other in the north direction (δon).
Corresponding displacement ductilities were also calculated for loading to the
south (µ∆-os) and to the north (µ∆-on).
The maximum useful displacements in the south and north directions for
this specimen were both 1.01 in. (25.6 mm). The corresponding drift ratios were
both 0.65 %, and the displacement ductilities were both 5.61. Figure 4.12 shows
how the maximum drift ratios in the south and north directions were determined
for Shear Wall Specimen 17.
-40
-30
-20
-10
0
10
20
30
40
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
Drift Ratio (%)
Bas
e Sh
ear
(Kip
s)
-178
-134
-89
-45
0
44
89
133
178
Bas
e Sh
ear
(KN
)
Maximum Selected Drift Ratio North
Maximum Selected Drift Ratio South
Figure 4.12: Selected drift ratios for Shear Wall Specimen 17
For Shear Wall Specimen 17, the response quantities discussed above are
given in Table 4.6.
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112
Table 4.6 Maximum displacements, ductilities and drift ratios for Shear Wall
Specimen 17
∆n
(in.) (mm)
∆s
(in.) (mm) µ∆-os µ∆-on δos (%) δon (%)
1.01 (25.6) 1.01 (25.6) 5.61 5.61 0.65 0.65
In the remainder of this section, the hysteretic behavior of Shear Wall
Specimen 17 as described above is summarized and compared with the
corresponding results for the flexure-dominated specimens discussed in Varela
(2003).
For initial tangent stiffness (Kot-o), initial backbone stiffness (Kob-o), and
for the ratio of initial backbone stiffness to initial tangent stiffness, values are
presented in Table 4.7. The results show that ratio of backbone stiffness versus
initial tangent stiffness for this specimen is consistent with the corresponding
mean value of those ratios for the specimens tested by Varela (2003). Differences
between the absolute stiffnesses obtained in this study and those obtained by
Varela (2003) are due to differences in material (f'AAC), geometry, and
reinforcement among specimens.
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113
Table 4.7 Comparison of initial tangent and backbone stiffnesses for flexure-
dominated specimens
Specimen
Number
Kot-o
Kips/in. (kN/mm)
Kob-o
Kips/in. (kN/mm) Kob-o /Kot-o
17 359.3 (63.0) 346.5 (60.7) 0.96 Specimens of
Varela (2003)
116.0 (20.3)
COV (75 %)
118.1 (20.7)
COV (56 %) 1.01
For secant stiffnesses after flexural cracking in the south (Kcr-os) and north
(Kcr-on) directions, and for the ratio of those observed secant stiffness after flexural
cracking to initial tangent stiffness, results are presented in Table 4.8. The results
show that ratio of secant stiffness versus initial tangent stiffness in both directions
for this specimen is consistent with the corresponding mean value of those ratios
for the specimens tested by Varela (2003).
Table 4.8 Comparison of secant stiffnesses after flexural cracking for flexure-
dominated specimens
Specimen
Number Kcr-os
Kips/in. (kN/mm) Kcr-os /Kot-o
Kcr-on
Kips/in. (kN/mm) Kcr-on /Kot-o
17 138.8 (24.3) 0.39 138.8 (24.3) 0.39
Specimens
of Varela
(2003)
50.2 (8.8)
COV (76 %)
0.45
COV (31 %) 59.2 (13.0)
COV (62 %)
0.42
COV (18 %)
For unloading stiffnesses after yielding of the flexural reinforcement in the
south (Ku-os) and north (Ku-on) directions, and for the ratio of those unloading
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114
stiffnesses to the initial tangent stiffness, values are presented in Table 4.9. The
ratios in both directions are consistent with the corresponding mean value of those
ratios for the specimens tested by Varela (2003).
Table 4.9 Comparison of unloading stiffnesses after yield of flexural
reinforcement in the south and north direction for flexure-dominated
specimens
Specimen
Number
Ku-os
Kips/in.
(kN/mm)
Ku-os/Kot-o Du-os/Dys
Ku-on
Kips/in.
(kN/mm)
Ku-on/Kot-o Du-on /Dyn
17 109.8
(19.45) 0.31 1.17 130.1 (23.0) 0.36 1.11
Specimens
of Varela
(2003)
37.0 (6.5)
COV (71 %)
0.35
COV (33 %)
1.58
COV
(34 %)
35.1 (6.15)
COV
(56 %)
0.27
COV
(28 %)
1.66
COV
(33 %)
For the stiffnesses after yield of flexural reinforcement in the south (Ky-os)
and north (Ky-on) directions, and for the ratio of those stiffnesses to initial tangent
stiffness, values are presented in Table 4.10. The ratios in both directions are
consistent with the corresponding mean values of those ratios for the specimens
tested by Varela (2003).
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115
Table 4.10 Comparison of stiffnesses after yield of flexural reinforcement for
flexure-dominated specimens
Specimen
Number
Ky-os
Kips/in. (kN/mm) Ky-os /Kot-o
Ky-on
Kips/in. (kN/mm) Ky-on /Kot-o
17 9.0 (1.59) 0.025 7.0 (1.24) 0.019 Specimens of
Varela (2003) 1.88 (0.33)
COV (59 %)
0.021
COV (47 %) 2.08 (0.67)
COV (74 %)
0.018
COV (52 %)
Maximum useful global drift ratios and corresponding displacement
ductilities are presented in Table 4.11. Shear Wall Specimen 17 had a higher
ductility in both directions than the other flexure-dominated specimens, probably
due to the helical ties used to connect the end units with the rest of the wall.
Table 4.11 Maximum useful displacement drift ratios and ductilities for flexure-
dominated specimens
Specimen
Number δos (%) δon (%) µ∆-os µ∆-on
17 0.65 0.65 5.6 5.6 Specimens
of Varela
(2003)
1.37
COV (32 %)
0.9
COV (31 %)
5.2
COV (9 %)
3.78
COV (43 %)
The capacity of Shear Wall Specimen 17 was governed by its nominal
flexural capacity. The hysteretic loops showed a similar pattern for loading and
unloading. The pinching was due to flexure-shear cracks.
Comparison of hysteretic behavior observed for Shear Wall Specimen 17
with that previously observed by Varela (2003) shows that the behaviors are
generally consistent, so that the values of R and Cd previously proposed by Varela
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116
can be safely used with flexure-dominated specimens of low-strength AAC. This
is true even though εAAC max is slightly lower than 0.003 for low-strength AAC.
4.2.2 Hysteretic Behavior of Shear-Dominated Specimens
The hysteretic load-displacement response of shear-dominated specimens
can be described in terms of the following:
• initial stiffness;
• stiffness after flexural cracking;
• unloading stiffness after web-shear cracking; and
• strength degradation after web-shear cracking.
Initial tangent and backbone stiffnesses were calculated for each shear-
dominated wall specimen, as for the flexure-dominated specimens (Figure 4.13).
The secant stiffness after flexural cracking was calculated as the applied load at
which web-shear cracking was first observed, divided by the corresponding
horizontal displacement. Fws1 and Dws1 are the load and displacement at which
web-shear cracking was first observed in the south direction, and Fwn1 and Dwn1
are the corresponding values in the north direction. Two secant stiffnesses were
calculated for each shear-dominated specimen; one in the south direction (Kcr-os)
and the other in the north direction (Kcr-on) (Figure 4.14). The unloading stiffness
after web shear cracking was calculated using the tangent to the load-
displacement curve on first unloading after observed web-shear cracking (Figure
4.15). Two unloading stiffnesses were calculated for each shear-dominated
specimen, one corresponding to displacements in the south direction (Ku-os) and
the other to displacements in the north direction (Ku-on). Du-os and Du-on are the
maximum observed displacements in the load cycles at which those unloading
stiffnesses were calculated in the south and north directions respectively. The
strength ratio after web shear cracking was calculated as the maximum applied
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117
load in the corresponding next cycle after web shear cracking divided by the
applied load at which web shear cracking was first observed during the test. Fws2
and Fwn2 are the maximum loads in the following cycle after web shear cracking
was first observed in the south and north directions respectively, and Dws2 and
Dwn2 are the displacements corresponding to those loads. Two strength ratios were
calculated for each shear-dominated specimen, one for loading to the south, and
the other to the north.
4.2.2.1 Shear Wall Specimen 18
The initial tangent stiffness and the initial backbone stiffness of Shear
Wall Specimen 18 were 300.7 kips/in. (52.7 kN/mm) and 299.5 kips/in. (52.5
kN/mm) respectively (Figure 4.13).
-20
-15
-10
-5
0
5
10
15
20
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Displacement (in.)
Bas
e Sh
ear
(kip
s)
-89
-67
-44
-22
0
22
44
67
89-5.08 -3.81 -2.54 -1.27 0 1.27 2.54 3.81 5.08
Displacement (mm)
Bas
e Sh
ear
(kN
)
Kot-o
Kob-o Initial Backbone Stiffness
Initial Tangent Stiffness
Figure 4.13: Initial tangent and backbone stiffnesses for Shear Wall Specimen
18
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The web-shear cracking load in the north direction was 35.66 kips (158.7
kN); the horizontal displacement was 0.18 in. (4.6 mm); and the corresponding
stiffness after flexural cracking was 198.1 kips/in. (34.7 kN/mm). In the south
direction, the corresponding values were 36.07 kips (164.58 kN), 0.24 in. (6.1
mm), and 150.3 kips/in.(26.4 kN/mm). Figure 4.14 shows secant stiffnesses after
flexural cracking for Shear Wall Specimen 18.
-40
-30
-20
-10
0
10
20
30
40
-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40
Displacement (in.)
Bas
e Sh
ear
(kip
s)
-178
-134
-89
-45
0
44
89
133
178-10.16 -7.62 -5.08 -2.54 0 2.54 5.08 7.62 10.16
Displacement (mm)
Bas
e Sh
ear
(kN
)
Kcr-os
Kcr-on
Stif fness AfterFlexural CrackingSouth
Web Shear Cracking North
Web Shear Cracking South
Stif fness AfterFlexural CrackingNorth
Figure 4.14: Secant stiffnesses after flexural cracking for Shear Wall Specimen
18
The unloading stiffnesses after web-shear cracking in the south and north
directions were 138.6 kips/in. (24.3 kN/mm) and 140.0 kips/in. (24.55 kN/mm)
respectively (Figure 4.15).
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-40
-30
-20
-10
0
10
20
30
40
-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40
Displacement (in.)
Bas
e Sh
ear
(kip
s)
-178
-134
-89
-45
0
44
89
133
178-10.16 -7.62 -5.08 -2.54 0 2.54 5.08 7.62 10.16
Displacement (mm)
Bas
e Sh
ear
(kN
)Ku-os
Ku-on
Unloading Stif fness AfterWeb Shear Cracking North
Unloading Stiffness AfterWeb Shear Cracking South
Figure 4.15: Unloading stiffnesses after web shear cracking for Shear Wall
Specimen 18
The maximum capacity in the next cycle in the south direction after web-
shear cracking was first observed in that same direction was 39 kips (173 kN), at a
horizontal displacement of 0.31 in. (7.8 mm), and the corresponding strength ratio
between the observed web-shear cracking load and the maximum observed load at
the next cycle was 1.08. The corresponding values for the north direction were
37.9 kips (168.9 kN), 0.26 in. (6.6 mm), and 1.06. Both sets of values are shown
in Figure 4.16 for Shear Wall Specimen 18. The complete hysteretic load-
displacement response of Shear Wall Specimen 18 at the end of the test is
presented in Figure 4.17.
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-50
-40-30
-20
-10
010
20
3040
50
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Displacement (in.)
Bas
e Sh
ear
(kip
s)
-222
-178-133
-89
-440
44
89
133178
222-15.24 -10.16 -5.08 0 5.08 10.16 15.24
Displacement (mm)
Bas
e Sh
ear
(kN
)
Web Shear Cracking South
Web Shear Cracking North
Maximum Load AfterWeb Shear Cracking North Maximum Load After
Web Shear Cracking South
Figure 4.16: Maximum applied load after web shear cracking in the south and
north directions for Shear Wall Specimen 18
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-50
-40
-30
-20
-10
0
10
20
30
40
50
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Drift Ratio (%)
Bas
e Sh
ear
(kip
s)
-222
-178
-133
-89
-44
0
44
89
133
178
222
Bas
e Sh
ear
(kN
)
Figure 4.17 Load- displacement response of Shear Wall Specimen 18
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4.2.2.2 Shear Wall Specimen 19
The initial tangent stiffness and the initial backbone stiffness of Shear
Wall Specimen 19 were 586.1 kips/in. (102.8 kN/mm) and 548.3 kips/in. (96.1
kN/mm) respectively (Figure 4.18).
-40
-30
-20
-10
0
10
20
30
40
-0.10 -0.08 -0.05 -0.03 0.00 0.03 0.05 0.08 0.10
Displacement (in.)
Bas
e S
hear
(Kip
s)
-178
-134
-89
-45
0
44
89
133
178-2.54 -2.03 -1.52 -1.02 -0.51 0.00 0.51 1.02 1.52 2.03 2.54
Displacement (mm)
Bas
e Sh
ear
(kN
)
Kot-o
Kob-oInitial TangentStif fness
Initial BackboneStif fness
Figure 4.18: Initial tangent and backbone stiffnesses for Shear Wall Specimen
19
The web-shear cracking load in the north direction was 54.84 kips (243.9
kN), at a horizontal displacement of 0.13 in. (3.3 mm). The corresponding
stiffness after flexural cracking was 421.8 kips/in. (73.9 kN/mm). In the south
direction, the corresponding values were 56.00 kips (249.1 kN), 0.19 in. (4.8
mm), and 294.7 kips/in. (51.7 kN/mm). Figure 4.19 shows both secant stiffnesses
after flexural cracking for Shear Wall Specimen 19.
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-80
-60
-40
-20
0
20
40
60
80
-0.60 -0.45 -0.30 -0.15 0.00 0.15 0.30 0.45 0.60
Displacement (in.)
Bas
e S
hear
(Kip
s)
-356
-267
-178
-89
0
89
178
267
356-15.24 -11.43 -7.62 -3.81 0.00 3.81 7.62 11.43 15.24
Displacement (mm)
Bas
e Sh
ear
(kN
)
Kcr-os
Kcr-on
Stif fness AfterFlexural CrackingSouth
Stiffness AfterFlexural CrackingNorth
Web Shear CrackingSouth
Web Shear CrackingNorth
Figure 4.19: Secant stiffnesses after flexural cracking for Shear Wall Specimen
19
The unloading stiffnesses after web-shear cracking in the south and north
directions were 227.6 kips/in. (39.9 kN/mm) and 320.7 kips/in. (56.25 kN/mm)
respectively (Figure 4.20).
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-80
-60
-40
-20
0
20
40
60
80
-0.60 -0.45 -0.30 -0.15 0.00 0.15 0.30 0.45 0.60
Displacement (in.)
Bas
e S
hear
(Kip
s)
-356
-267
-178
-89
0
89
178
267
356-15.24 -11.43 -7.62 -3.81 0.00 3.81 7.62 11.43 15.24
Displacement (mm)
Bas
e Sh
ear
(kN
)
Ku-os
Ku-on
Unloading Stif fnessAfter Web ShearCracking South
Unloading Stif fnessAfter Web ShearCracking North
Figure 4.20: Unloading stiffnesses after web-shear cracking for Shear Wall
Specimen 19
The maximum capacity in the south direction in the next cycle after web
shear-cracking was first observed in that direction was 56.78 kips (255 kN), at a
displacement of 0.25 in. (6.4 mm), and the corresponding strength ratio between
the observed web-shear cracking load and the maximum observed load at the next
cycle was 1.01. In the north direction, the corresponding values were 59.5 kips
(267.9 kN), 0.20 in. (5.1 mm), and 1.08. Both maximum applied loads in the next
corresponding cycles after web-shear cracking are shown in Figure 4.21 for Shear
Wall Specimen 19. The complete hysteretic load-displacement response of Shear
Wall Specimen 19 at the end of the test is presented in Figure 4.22.
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-80
-60
-40
-20
0
20
40
60
80
-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00
Displacement (in.)
Bas
e S
hear
(Kip
s)
-356
-267
-178
-89
0
89
178
267
356-25.40 -20.32 -15.24 -10.16 -5.08 0.00 5.08 10.16 15.24 20.32 25.40
Displacement (mm)
Bas
e Sh
ear
(kN
)
Maximum Load AfterWeb Shear CrackingNorth Maximum Load After
Web Shear CrackingSouth
Web Shear CrackingNorth
Web Shear CrackingSouth
Figure 4.21: Maximum applied load after web-shear cracking in the south and
north directions for Shear Wall Specimen 19
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-80
-60
-40
-20
0
20
40
60
80
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Drift Ratio (%)
Bas
e S
hear
(Kip
s)
-356
-267
-178
-89
0
89
178
267
356
Bas
e Sh
ear
(kN
)
Figure 4.22 Load-displacement response of Shear Wall Specimen 19
4.2.2.3 Summary of Results for Shear Wall Specimens 18 and 19
In this section, the hysteretic behavior of Shear Wall Specimens 18 and 19
is compared with that of the shear-dominated specimens of Varela (2003).
The observed initial tangent stiffness (Kot-o), initial backbone stiffness
(Kob-o), and the ratio of the initial backbone stiffness to initial tangent stiffness for
Shear Wall Specimens 18 and 19, are compared in Table 4.12 with the
corresponding mean value of the shear-dominated specimens tested by Varela
(2003). The ratio of observed backbone stiffness to initial tangent stiffness of the
Shear Wall Specimens 18 and 19 is consistent with the corresponding mean value
of the specimens tested by Varela (2003). The difference between the absolute
stiffnesses obtained in this study and the corresponding to those of the specimens
tested by Varela (2003) are due to differences in material (f'AAC), geometry, and
reinforcement.
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Table 4.12 Observed initial tangent and backbone stiffnesses for shear-
dominated specimens
Specimen
Number
Kot-o
Kips/in. (kN/mm)
Kob-o
Kips/in. (kN/mm) Kob-o /Kot-o
18 300.7 (52.7) 299.5 (52.5) 0.99 19 586.1 (102.8) 548.3 (96.1) 0.94
Specimens of
Varela (2003)
464.6 (81.5)
COV (65 %)
459.4 (80.6)
COV (65 %)
0.98
The observed secant stiffnesses after flexural cracking in the south (Kcr-os)
and north (Kcr-on) directions, and the ratio of those observed secant stiffness after
flexural cracking to initial tangent stiffness for Shear Wall Specimens 18 and 19
and the corresponding mean value of the shear-dominated specimens tested by
Varela (2003), are presented in Table 4.13. The ratios are consistent with the
corresponding mean values of the specimens tested by Varela (2003).
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Table 4.13 Secant stiffnesses after flexural cracking for shear-dominated
specimens
Specimen
Number
Kcr-os
Kips/in. (kN/mm) Kcr-os /Kot-o
Kcr-on
Kips/in. (kN/mm) Kcr-on /Kot-o
18 150.3 (26.4) 0.50 198.1 (34.7) 0.6619 294.7 (51.7) 0.50 421.8 (73.9) 0.72
Specimens of
Varela (2003) 263.1 (46.1)
COV (88 %) 0.56
347.1 (60.8)
COV (74 %) 0.75
The unloading stiffnesses after web shear cracking in the south (Ku-os), and
north (Ku-on) directions, and the ratio of those unloading stiffnesses to the initial
tangent stiffness for Shear Wall Specimen 18 and 19 and the corresponding mean
value of the shear-dominated specimens tested by Varela are presented in Table
4.14. The ratios are consistent with the corresponding mean values of the
specimens tested by Varela (2003).
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Table 4.14 Unloading stiffnesses after web shear cracking in the south and
north direction for shear-dominated specimens
Specimen
Number
Ku-os
Kips/in.
(kN/mm)
Ku-os/Kot-o Du-os/Dws1
Ku-on
Kips/in.
(kN/mm)
Ku-on/Kot-o Du-on /Dwn1
18 138.6 (24.3) 0.46 1.17 140.0 (24.5) 0.47 1.38
19 227.6 (39.9) 0.39 1.15 320.7 (56.3) 0.54 1.39
Specimens
of Varela
(2003)
280.1 (49.1)
COV
(73 %)
0.60
1.15
COV
(15 %)
298.1 (52.2)
COV
(75 %)
0.64
1.19
COV
(17 %)
The strength ratio after web shear cracking and the ratio of the horizontal
displacement at the maximum applied load in the corresponding next cycle after
web shear cracking, to the horizontal displacement at web shear cracking in the
south and north directions for Shear Wall Specimens 18 and 19, are compared in
Table 4.15 with the corresponding mean value of the shear-dominated specimens
tested by Varela (2003). The strength ratios after web shear cracking in both south
and north directions of Shear Wall Specimens 18 and 19 are similar. The strength
ratios after web shear cracking in both south and north directions for Shear Wall
Specimens 18 and 19 are consistent with the corresponding mean values of the
specimens tested by Varela (2003).
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Table 4.15 Strength ratios after web shear cracking and corresponding
displacement ratios for shear-dominated specimens
Specimen
Number Fws2 /Fws1 Dws2 /Dws1 Fwn2 /Fwn1 Dwn2 /Dwn1
18 1.08 1.29 1.06 1.44
19 1.01 1.32 1.08 1.54
Specimens of
Varela (2003) 0.94
COV (26 %)
1.51
COV (28 %) 0.91
COV (34 %)
1.66
COV (22 %)
The shear capacity of Shear Wall Specimens 18 and 19 was governed by
crushing of the diagonal strut. The overall hysteretic behavior of these two
specimens was characterized by a sudden degradation in stiffness after web-shear
cracking, and showed a behavior consistent with that of the shear-dominated
specimens tested by Varela (2003).
The main conclusion obtained from the comparison between the test
results and the predicted results is that the proposed design provisions for shear
capacity accurately predicted the capacities of shear-dominated Shear Wall
Specimens 18 and 19. This permits one to conclude that these design provisions,
originally developed for shear walls using higher-strength AAC specimens, are
valid for low-strength AAC specimens as well.
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CHAPTER 5 Summary, Conclusions and Recommendations
5.1 SUMMARY
The purpose of this study was to evaluate the results of reversed cyclic
load tests on 3 shear-wall specimens constructed with low-strength AAC
(autoclaved aerated concrete). One shear wall specimen (SWS17) was designed to
exhibit flexure-dominated behavior; the other two (SWS18 and SWS19) were
designed to exhibit shear-dominated behavior.
The flexure-dominated specimen was constructed with vertically oriented,
reinforced panels of low-strength AAC material. The objectives of this test were
to examine the specimen’s general hysteretic behavior, and to evaluate possible
improvements in that behavior due to stainless steel spiral ties connecting the
extreme-fiber elements to the remainder of the specimen.
The shear-dominated specimens were constructed with masonry-type units
of low-strength AAC material. The specimens, with aspect ratios (height to plan
length) of 0.71 and 1.34, had different arrangements of flexural reinforcement.
The objectives of these tests were to examine the specimens’ overall hysteretic
behavior and to validate the applicability to low-strength AAC shear walls, of
proposed design provisions previously developed based on shear-wall and
assemblage tests with higher-strength AAC material. The overall hysteretic
behavior of the specimens tested in this study was compared with the
corresponding behavior of those specimens tested by Varela (2003). The results
obtained with the proposed design provisions for the different capacities of the
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specimens tested in this study were compared with the corresponding mean values
of those specimens tested by Tanner (2003).
In each test, quasi-static reversed cyclic loads were applied to each
specimen, and the major events and overall hysteretic behavior were evaluated.
After each test, overall damage was summarized; major events and hysteretic
behavior were compared with predicted responses; and maximum drift ratios and
displacement ductilities were assessed.
This study is the final facet of an extensive research project performed at
the Ferguson Structural Engineering Laboratory of The University of Texas at
Austin, using results from that and other testing laboratories (Tanner 2003, Varela
2003, Argudo 2003).
5.2 CONCLUSIONS
1) Previously proposed design provisions for nominal flexural capacity
accurately predicted the capacity of flexure-dominated Shear Wall
Specimen 17, and therefore are valid for low-strength AAC specimens as
well as the higher-strength AAC specimens originally used to develop
those provisions.
2) The maximum useful strain obtained in this study for low-strength AAC
was less than the value of 0.003 reported by Tanner (2003). In fact, the
maximum useful strain decreases with decreasing compressive strength,
and was between 0.0015 and 0.002 for low-strength AAC. Because that
capacity is governed by the mechanical characteristics of the
reinforcement in all practical cases, regardless of the value of εAAC max ,
previously proposed expressions for nominal flexural capacity are still
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133
valid. Previously proposed expressions for AAC modulus as a function of
specified compressive strength are also valid.
3) Stainless steel spiral ties, used to connect the end U-blocks of Shear Wall
Specimen 17 to the vertical panels comprising the rest of the wall,
significantly reduced deterioration of the compression toes of that
specimen under cycles of reversed cyclic load. The specimen achieved
in-plane lateral drift ratios of 0.65 % and lateral ductilities of 5 in both
directions.
5) Previously proposed design provisions for web-shear capacity accurately
predicted the capacity of shear-dominated Shear Wall Specimens 18 and
19, and therefore are valid for low-strength AAC specimens as well as the
higher-strength AAC specimens originally used to develop those
provisions.
6) The shear capacity of Shear Wall Specimens 18 and 19 was governed by
crushing of the diagonal strut, at a drift ratio of 0.37 % (loading to the
north) for Shear Wall Specimen 18 and 0.26 % (loading to the north) for
Shear Wall Specimen 19.
7) The overall hysteretic behavior of the shear-dominated specimens (SWS18
and SWS19) was characterized by a sudden degradation in stiffness after
web-shear cracking and showed a behavior consistent with that of the
shear-dominated specimens tested by Varela (2003). The maximum drift
ratios obtained for Shear Wall Specimens 18 and 19 were 0.48 % and
0.49 % in both directions respectively.
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8) The ductilities and drifts obtained in this study are consistent with those
obtained by Varela (2003) for flexure-dominated shear walls of higher-
strength AAC material, in spite of the lower maximum useable strain of
the low-strength AAC. Therefore, the R and Cd values proposed by Varela
(2003) are valid for low-strength AAC material as well.
9) Based on the close agreement obtained between observed and predicted
values for capacities and stiffnesses, the analytical models used to represent
the behavior of shear-dominated and flexure-dominated specimens,
constructed with AAC material of medium and high compressive strength,
are also applicable to specimens constructed with AAC material of low
compressive strength.
5.3 RECOMMENDATIONS FOR FUTURE WORK
1) Additional testing should be performed on AAC shear walls with
openings. Such testing would provide information about the behavior
(limit states) of AAC walls with openings compared to the capacity
predictions of current design provisions.
2) Additional work should be performed to develop strut-and-tie models for
AAC walls. These models would offer the possibility of simplified design
approaches by combining web-shear cracking, flexure-shear cracking and
crushing of the diagonal strut, in a single design model.
3) Additional research should be performed on ways to use grouted regions
within AAC shear walls to increase their resistance to flexural
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compression, to crushing of the diagonal strut, and perhaps to sliding.
Possible failure at the interface between the AAC material and the grout
can be avoided using spiral ties. The purpose of this research would be to
improve the strength and ductility of AAC shear walls.
4) Additional research should be conducted on the behavior and design of
AAC infill panels in frames of structural steel or reinforced concrete. Such
infills could increase the strength, stiffness and energy dissipation capacity
of framed structures, in retrofit as well as new construction.
5) Additional research should be conducted on increasing the sliding-shear
capacity of AAC shear walls. This would result in AAC structures with
higher factors of safety against sliding in zones with large spectral
ordinates.
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APPENDIX A Design Provisions for Reinforced AAC Shear
Walls
A.1 DESIGN OF AAC SHEAR WALLS
Appendix A was originally developed as part of the PhD dissertation of
Tanner (2003). It is included here so that the reader will be able to see the context
in which the design provisions discussed in this thesis were originally proposed.
A suite of 14 AAC shear wall specimens, with aspect ratios (height of the
point of load application divided by the plan length) from 0.6 to 3, has been tested
at the University of Texas at Austin. The behavior of each shear wall may be
shear- or flexure-dominated. The shear-dominated specimens were heavily
reinforced in flexure using external reinforcement. The flexure-dominated
specimens were lightly reinforced in flexure. The test setup is shown in Figure
A.1.
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Rams for load maintainerTie down
boxes for rods
Axial load system
Tie down boxes for rods
External reinforcement
External reinforcementRams
for load maintainerTie down
boxes for rods
Axial load system
Tie down boxes for rods
External reinforcement
External reinforcement
Figure A.1 Test set up for shear wall specimens (UT Austin)
Physical details for each specimen are presented in Table A.1. The
number after the supplier’s name identifies in which shipment the AAC material
arrived.
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Table A.1 Details of shear wall specimens tested at UT Austin
Specimen
Failure Mode
AAC units
Materialsupplier
Length in. (m)
Height in. (m)
Thickness in. (m)
Aspect Ratio
Interior Vertical
Reinforcement1 Shear Horiz. Panels Contec 1 240 (6.1) 154 (3.9) 8 (0.2) 0.64 No 2 Shear Vert. Panels Ytong 1 240 (6.1) 154 (3.9) 8 (0.2) 0.64 No 3 Shear Blocks Ytong 2 240 (6.1) 151 (3.8) 8 (0.2) 0.63 No
4 Shear Horiz. Panels Matrix 1 240 (6.1) 154 (3.9) 8 (0.2) 0.64 #5 (16 mm) at 48 in. (1.2 m)
5 Shear Blocks Contec 2 240 (6.1) 151 (3.8) 8 (0.2) 0.63 No 7 Shear Blocks Ytong 2 144 (3.7) 151 (3.8) 8 (0.2) 1.05 No 9 Shear Horiz. Panels Matrix 1 96 (2.4) 154 (3.9) 8 (0.2) 1.60 No
11 Shear Blocks Contec 2 48 (1.2) 151 (3.8) 8 (0.2) 3.15 No
13 Flexure Horizontal
Panels Ytong 1 72 (2.1) 154 (3.9) 8 (0.2) 2.13
# 5 (16 mm) 12 in. (0.6 m) from
ends
14a Flexure Horizontal
Panels Babb 1 56 (1.4) 154 (3.9) 10 (0.3) 3.2 # 5 (16 mm) 4 in. (0.1 m) from ends
14b Flexure Horizontal
Panels Babb 1 56 (1.4) 154 (3.9) 10 (0.3) 3.2 # 5 (16 mm) 4 in. (0.1 m) from ends
15a Flexure
Vertical Panels with End Blocks Babb 1 112 (2.8) 154 (3.9) 10 (0.3) 1.4
# 5 (16 mm) 8 in. (0.2 m) from ends
15b Flexure
Vertical Panels with End Blocks Babb 1 112 (2.8) 154 (3.9) 10 (0.3) 1.4
# 5 (16 mm) 8 in. (0.2 m) from ends
16 Flexure
Vertical Panels with U End
Blocks Babb 1 112 (2.8) 154 (3.9) 10 (0.3) 1.4 # 5 (16 mm) 8 in. (0.2 m) from ends
17 Flexure
Vertical Panels with U End
Blocks Babb 2 112 (2.8) 154 (3.9) 10 (0.3) 1.4 # 5 (16 mm) 8 in. (0.2 m) from ends
Results from a suite of 12 shear-wall tests performed by Hebel (Germany)
provide additional information1. Each of those walls measured 8.2 ft (2.5 m)
long, 8.2 ft (2.5 m) tall and 9.5 in. (0.24 m) thick. The aspect ratio of each
specimen is 1.0. The test set up is shown in Figure A.2. Additional physical
details for each Hebel specimen are presented in Table A.2.
1 Personal communication, Violandi Vratsanou, Hebel AG, Germany, November 2000
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Rods for applied axial load
External reinforcing rods
Rods for applied axial load
External reinforcing rods
Figure A.2 Test setup for shear wall specimens at Hebel (Germany)
Table A.2 Details of shear wall specimens tested by Hebel (Germany)
Specimen
AAC Units
Mortared Head Joints
Type of Running
Bond 3.3 Blocks No one-half 3.2 Blocks No one-half 3.4 Blocks No one-half 3.5 Blocks No one-fifth 3.6 Blocks Yes one-fifth 4.3 Blocks No one-half 4.4 Blocks No one-half 4.1 Blocks No one-half 4.5 Blocks No one-fifth 4.6 Blocks No one-fifth 4.7 Blocks Yes one-fifth 4.8 Blocks Yes one-fifth
In the Hebel tests, axial load was applied using uniformly spaced, external
post-tensioning rods. This axial load was monitored and was kept constant. Two
additional 1 in. (25 mm) diameter rods on each side of the wall, with initial pre-
tension less than 0.5 kip (2 kN), were used as external reinforcement. As the wall
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displaces laterally in its own plane, tensile forces increase in the external
reinforcement on the tension side. The rods on the compressive side of the wall
are not initially post-tensioned, so the force in them does not decrease as the force
in the tension rods increases. Increasing the force in the tension rods without
decreasing the force in the compression rods is equivalent to applying an
additional compressive axial load to the wall. Therefore, the axial load in the
Hebel specimens changed as the lateral load changed. The axial load used to
evaluate the behavior of the Hebel specimens at each state is the initial axial load
(including weight of loading equipment) plus the summation of tensile forces in
the rods at that state.
A.1.1 Web-shear Cracking
Using additional data points determined at UT Austin between November
2001 and August 2002, the relationship between splitting tensile strength and
“1386 density” presented in Equation (A.1) has been replaced by
AACt ff '4.2= . As discussed in this section, that difference in splitting tensile
strength is less a few percent, and the actual change in computed values of VAAC is
quite small.
This section is dedicated to explaining the changes. The form of the
equation for VAAC will stay the same, with only slight changes in the external
coefficients. In the following section, the derivation of the equation for web-shear
cracking is reviewed.
tf
PftV
wAAC
uAACwAAC
ll
'
'
4.219.0 += Equation (A.1)
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tf
PftV
wAAC
uAACwAAC
ll
'
'
4.216.0 += Equation (A.2)
tfP
ftVwt
utwAAC
ll += 137.0 Equation (A.3)
tfP
ftVwt
utwAAC
ll += 125.0 Equation (A.4)
This inclined crack forms when the principal tensile stress in the web
exceeds the tensile strength of the AAC. That principal stress is given by
Equation (A.5), in which the normal stress in the wall is n and the maximum shear
stress in the center of the web is v.
( )2nv
2nf 2
2
t −
+
= where
t2l3Vv
w
= and tl
Pnw
= Equation (A.5)
Substituting the equations for shear stress and axial stress into the above
equation, and solving for the shear, the corresponding shear capacity is given by
Equation (A.6):
0.5
wtt
wAAC tlf
P1f3
t2lV
+⋅= Equation (A.6)
For reinforced concrete shear walls, ACI 318-02 uses a conservative (low)
diagonal tensile capacity of cf4 ′ (US customary units) to develop a
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142
conservative, semi-empirical equation for shear capacity as governed by web-
shear cracking (ACI 318-02).
Web-shear cracking was observed in all AAC shear-wall specimens tested
at The University of Texas at Austin except Shear Wall Specimen 2 (constructed
of vertical panels). In addition, the tests performed by Hebel (Germany) provide
corroborating data on shear strength as controlled by web-shear cracking. The
observed and predicted web-shear cracking capacities based on Equation (A.6)
are presented in Table A.3 and Table A.4 for fully and partially mortared
specimens respectively.
Table A.3 Initial predictions of capacity as governed by web-shear cracking for
fully mortared specimens
Specimen Axial load, P
kips (kN) Observed VAAC
kips (kN) Predicted VAAC
kips (kN) Observed VAAC / Predicted VAAC
1 (UT) 156.0 (694) 164.2 (730) 127.7 (568) 1.29 3 (UT) 120.0 (534) 81.3 (362) 111.4 (495) 0.73 4 (UT) 120.0 (534) 110.5 (492) 132.5 (589) 0.83 5 (UT) 60.0 (267) 62.2 (277) 117.4 (522) 0.53 7 (UT) 80.0 (356) 57.4 (255) 68.7 (305) 0.84 9 (UT) 30.0 (267) 37.7 (168) 55.9 (249) 0.67
11 (UT) 25.0 (111) 15.6 (69) 26.9 (120) 0.58 Assemblage (UT) 25.0 (111) 52.0 (231) 96.7 (430) 0.54
3.6 (Hebel) 36.8 (164) 27.7 (123) 39.3 (175) 0.71 4.7 (Hebel) 62.4 (277) 46.7 (208) 57.7 (256) 0.81 4.8 (Hebel) 178.2 (792) 61.5 (273) 80.3 (357) 0.77
Mean 0.70 COV (%) 16.8
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Table A.4 Initial predictions of capacity as governed by web-shear cracking for
partially mortared specimens
Specimen Axial load, P
kips (kN) Observed VAAC
kips (kN) Predicted VAAC
kips (kN) Observed VAAC / Predicted VAAC
3.3 (Hebel) 60.0 (267) 18.3 (81) 36.2 (161) 0.50 3.2 (Hebel) 26.2 (116) 20.6 (92) 42.0 (187) 0.49 3.4 (Hebel) 49.7 (221) 24.4 (109) 52.2 (232) 0.47 3.5 (Hebel) 89.8 (399) 18.2 (81) 36.7 (163) 0.49 4.3 (Hebel) 30.3 (135) 23.7 (105) 49.4 (220) 0.48 4.4 (Hebel) 30.3 (135) 32.1 (143) 62.7 (279) 0.51 4.1 (Hebel) 85.5 (380) 25.1 (112) 76.7 (341) 0.33 4.5 (Hebel) 153.9 (685) 21.3 (95) 48.5 (216) 0.44 4.6 (Hebel) 33.5 (149) 29.9 (133) 74.5 (331) 0.40
Mean 0.46 COV (%) 13.1
The shear strength of the AAC shear-wall specimens was initially
predicted using Equation (A.6). The ratios of observed to predicted capacities,
shown in Table A.3, indicate that the ratio of observed strength to predicted
strength of Shear Wall Specimen 1 (UT Austin) is significantly greater than for
the other specimens, and can be considered an anomaly with respect to the rest of
the tests. The remaining specimens show lower observed than predicted
strengths, indicating that Equation (A.6) is unconservative.
To further evaluate the effects of mortared head joints, the AAC shear-
walls tested at UT Austin and by Hebel (Germany) are divided into two groups:
those with fully mortared head joints, and those with unmortared head joints. The
range of ratios of observed VAAC to predicted VAAC is 0.54 to 0.1.29 for the fully
mortared specimens, and 0.33 to 0.51 for the partially mortared specimens. For
the specimens with fully mortared head joints, the mean ratio of observed to
predicted VAAC is 0.70, with a coefficient of variation of 17%. For the specimens
with unmortared head joints, corresponding values are 0.46 and 13%.
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These data can be plotted in Figure A.3 and Figure A.4. In each figure,
the mean ratio of observed capacity to that predicted using the theoretical
Equation (A.6) is represented by a solid horizontal line. Also plotted on each
figure is the normal distribution with the same mean and COV as the test data.
The lower 10% fractile of that distribution, shown by a dashed horizontal line, has
a value of 0.55 for the fully mortared specimens and 0.38 for the partially
mortared ones.
Equation (A.6) was therefore reduced so that it would correspond to the
lower 10% fractiles of the ratios of observed to predicted capacities. In carrying
out that reduction, fully mortared and partially mortared specimens were
considered separately. Equation (A.6) was multiplied by 0.55 to obtain proposed
Equation (A.1) for fully mortared specimens. In the same way, Equation (A.6)
was multiplied by 0.38 to obtain proposed Equation (A.2) for partially mortared
specimens.
0.00.2
0.40.60.8
1.01.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Aspect Ratio
V obs
/ V A
AC
Mean10% Fractile
Figure A.3 Ratios of observed to predicted (Equation (A.6)) web-shear cracking
capacities for AAC shear-wall specimens with fully mortared head joints
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Aspect Ratio
Vob
s / V
AAC
Mean10% Fractile
Figure A.4 Ratios of observed to predicted (Equation (A.6)) web-shear cracking
capacities for AAC shear-wall specimens with partially mortared head joints
The predicted VAAC using Equation (A.1) and Equation (A.2) are presented
in Table A.5 and Table A.6.
Table A.6 shows the prediction of capacity for all specimens that exhibited
web-shear cracking. Ratios of observed VAAC versus predicted VAAC using
Equation (A.1) and Equation (A.2) based on the tested compressive strength are
presented in Figure A.5. In that figure, a solid diagonal line represents perfect
agreement between observed and predicted shear capacities. The proposed
equations are very close, or have slight errors in the direction of conservatism, for
the specimens tested. If the ACI 318-02 equation for web shear cracking is used
directly for AAC (substituting fAAC for fc), the predicted capacity is greater than
that observed, and hence unconservative. This is also true if the ACI 318-02
equation for web shear cracking is used with equivalent expressions for the tensile
strength of concrete and for AAC. The web-shear cracking capacity will be
further reduced by using the specified compressive strength rather than the tested
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146
compressive strength. These results for the specimens tested at UT Austin are
presented in Figure A.6. The one data point where the observed VAAC falls below
the predicted VAAC is the Two-story Assemblage Specimen where the tested
compressive strength fell below the specified compressive strength.
Table A.5 Prediction of capacity as governed by web-shear cracking for fully
mortared specimens (Equation (A.1)) using tested compressive strength
Specimen Axial load, P
kips (kN) Observed VAAC
kips (kN) Predicted VAAC
kips (kN) Observed VAAC / Predicted VAAC
1 (UT) 156.0 (694) 164.2 (730) 70 (312) 2.34 3 (UT) 120.0 (534) 81.3 (362) 61 (273) 1.33 4 (UT) 120.0 (534) 110.5 (492) 73 (324) 1.52 5 (UT) 60.0 (267) 62.2 (277) 65 (287) 0.96 7 (UT) 80.0 (356) 57.4 (255) 38 (168) 1.52 9 (UT) 30.0 (267) 37.7 (168) 31 (137) 1.22
11 (UT) 25.0 (111) 15.6 (69) 15 (66) 1.05 Assemblage (UT) 26.0 (116) 52.0 (231) 53 (237) 0.98
3.6 (Hebel) 36.8 (164) 27.7 (123) 22 (96) 1.28 4.7 (Hebel) 62.4 (277) 46.7 (208) 32 (141) 1.47 4.8 (Hebel) 178.2 (792) 61.5 (273) 44 (197) 1.39
Mean 1.27 COV (%) 16.8
Table A.6 Prediction of capacity as governed by web-shear cracking for
unmortared head joints (Equation (A.2)) using tested compressive strength
Specimen Axial load, P
kips (kN) Observed VAAC
kips (kN) Predicted VAAC
kips (kN) Observed VAAC / Predicted VAAC
3.3 (Hebel) 26.2 (116) 18.3 (81) 14 (61) 1.33 3.2 (Hebel) 49.7 (221) 20.6 (92) 16 (71) 1.29 3.4 (Hebel) 89.8 (399) 24.4 (109) 20 (88) 1.23 3.5 (Hebel) 26.6 (118) 18.2 (81) 14 (62) 1.30 4.3 (Hebel) 30.3 (135) 23.7 (105) 19 (84) 1.26 4.4 (Hebel) 85.5 (380) 32.1 (143) 24 (106) 1.35 4.1 (Hebel) 153.9 (685) 25.1 (112) 29 (130) 0.86 4.5 (Hebel) 33.5 (149) 21.3 (95) 18 (82) 1.15 4.6 (Hebel) 158.1 (703) 29.9 (133) 28 (126) 1.06
Mean 1.21 COV (%) 13.1
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0
40
80
120
160
200
0 40 80 120VAAC from Adjusted Equations 10% LF (kips)
Obs
erve
d V A
AC (k
ips)
0
178
356
534
712
8900 178 356 534
VAAC from Adjusted Equations 10% LF (kN)
Obs
erve
d V A
AC (k
N)
Fully MortaredHead Joints
Partially MortaredHead Joints
Figure A.5 Observed versus predicted capacities as governed by web-shear
cracking (Equation (A.1) and Equation (A.2)) using tested compressive strength
0
40
80
120
160
200
0 40 80 120
VAAC from Adjusted Equations 10% LF (kips)
Obs
erve
d V
AA
C (ki
ps)
0
178
356
534
712
8900 178 356 534
VAAC from Adjusted Equations 10% LF (kN)
Obs
erve
d V
AA
C (k
N)Fully Mortared
Head Joints
Figure A.6 Observed versus predicted capacities as governed by web-shear
cracking (Equation (A.1)) and Equation (A.2)) using specified compressive
strength
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A.1.2 Flexure-Shear Cracking for AAC Shear Walls
A flexure-shear crack begins as a horizontal crack at a height of about
one-half the plan length of the wall (lw) above the base of the wall, and then
propagates diagonally through the center of the wall, as shown in Figure A.7.
V
P
Figure A.7 Flexure-shear cracking
The formation of this crack is governed by the flexural tensile stress in the
wall (Equation (A.7)).
nx AN
SM
±=σ Equation (A.7)
Based on experiments with reinforced concrete shear walls, the controlling
horizontal crack develops at a height of about lw/2. Therefore, the moment at the
crack, Mflcr is:
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2w
flcrVlMM −= Equation (A.8)
where M is the moment at the base. Equation (A.9) presents the base
shear at the formation of the flexural portion of the flexure-shear crack:
2w
wrx
flcr lVM
tlNfS
V−
+
=
Equation (A.9)
ACI 318-02 uses a conservative (low) flexural tensile strength of
cf6 ′ (US customary units) substituted into Equation (A.9); experiments have
shown an additional force of tdf0.6 c ⋅′ is required to develop the crack.
Therefore, ACI 318-02 uses Equation (A.10) for the flexure-shear cracking
capacity.
td
2l
VM
tlN0.21f1.25l
f0.6Vw
wcw
cc ⋅
−
+′
+′=
Equation (A.10)
Flexure-shear cracking was not observed in the 8 shear-dominated shear
wall specimens tested at UT Austin because the exterior unbonded reinforcement
(threaded rods) prevents vertical tensile stresses from forming at the base of the
wall after flexural cracking (see Figure A.1). Flexure-shear cracking was
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observed in the 6 flexure-dominated shear wall specimens. In every case the
flexural portion of the flexure-shear crack formed first in the horizontal joint.
Based on the location of the flexural crack, the predicted load can be
determined based on Equation (A.9) (see Table A.7). For AAC the modulus of
rupture was calculated using tr f2f ⋅= , and the tested splitting tensile strength.
This value was used in Equation (A.9). For flexure-dominated shear wall
specimens, with the exception of Shear Wall Specimen 14a, the ratio of observed
load versus predicted load ranges from 0.6 to 1.3. The mean ratio is 0.86 with a
COV of 36%.
The observed load is lower than the predicted load because the failure
occurred in the joint between the AAC and the thin-bed mortar rather than in the
AAC material itself. A relationship for the tensile bond strength fbond between
AAC and thin-bed mortar was determined based on tests performed at UAB was
presented in Section 3.6.2. Equation (A.11) presents the tensile bond strength for
AAC densities greater than 32 pcf (2 kg/m3). This indicates that for mid- to high-
density AAC the tensile bond strength, fbond, will be lower than the modulus of
rupture. The tensile bond strength of the material in the flexure-dominated
specimens except Shear Wall Specimen 13, is 94 psi (0.7 MPa) based on a density
of 39.9 pcf (2.5 kg/m3). Shear Wall Specimen 13 had a density below the limit of
32 pcf; therefore the modulus of rupture will govern the formation of a flexure-
shear crack. The results of using the tensile bond strength rather than the modulus
of rupture in Equation (A.9) for the remaining specimens are presented in Table
A.8. With the exception of Shear Wall Specimen 14a, the ratios of observed to
predicted strength range from 1.0 to 1.3 with a mean of 1.15 and a COV of 6.5%.
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Shear Wall Specimen 14a exhibited flexural cracks at the base of the wall
prior to testing. These cracks are presumed to have occurred while moving the
top of the wall (out-of-plane) approximately 1 in. (25 mm) to the east to align the
rams and loading beam. This would be expected to cause premature out-of-plane
flexural cracks on the west side of the wall, which is where the first flexure-shear
cracks did in fact occur.
34ρ1.5fbond +⋅=
ρ in lb/ft3 , and fbond in lb/in.2 Equation (A.11)
6604.0 +⋅= AACbond ff
fAAC and fbond in lb/in.2 Equation (A.12)
Table A.7 Results for flexure-shear cracking of AAC flexure-dominated shear
wall specimens
Specimen fr N
kips (kN)
Tested Vflcr North
kips (kN)
Predicted Vflcr NorthKips (kN)
Tested VflcrSouth
kips (kN)
Predicted Vflcr South kips (kN)
Observed Vflcr/Predicted
Vflcr North Kips (kN)
Observed Vflcr/Predicted
Vflcr North kips (kN)
13 110 (0.8) 25 (111) 9.6 (43) 8.2 (36) 10.1 (45) 8.0 (36) 1.18 1.26
14a 178 (1.2) 5 (22) N/A N/A 2.8 (12) 7.4 (33) N/A 0.38
14b 178 (1.2) 5 (22) 4.9 (22) 7.4 (33) 4.6 (20) 7.4 (33) 0.66 0.62
15a 178 (1.2) 25 (111) 21.5 (96) 31.9 (142) 24.0 (107) 39.1 (174) 0.71 0.61
15b 178 (1.2) 25 (111) 20.0 (89) -17.9 (-80) 17.5 (78) 17.1 (76) 0.66 0.60
16 178 (1.2) 25 (111) -24.0 (-107) 31.9 (142) 21.8 (97) 32.4 (144) 0.75 0.67
Mean 0.86
COV (%) 36.1
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Table A.8 Results for flexure-shear cracking of AAC flexure-dominated shear
wall specimens using tensile bond strength of material
Specimen fbond P
kips (kN)
Tested Vflcr North
kips (kN)
Predicted Vflcr NorthKips (kN)
Tested Vflcr South
kips (kN)
Predicted Vflcr South kips (kN)
Observed Vflcr/Predicted
Vflcr North Kips (kN)
Observed Vflcr/Predicted
Vflcr North kips (kN)
13 110 (0.8) 25 (111) 9.6 (43) 8.2 (36) 10.1 (45) 8.0 (36) 1.18 1.26
14a 94 (0.7) 5 (22) N/A N/A 2.8 (12) 4.1 (18) N/A 0.68
14b 94 (0.7) 5 (22) 4.9 (22) 4.1 (18) 4.6 (20) 4.1 (18) 1.19 1.11
15a 94 (0.7) 25 (111) 21.5 (96) 18.7 (83) 24.0 (107) 22.9 (102) 1.15 1.05
15b 94 (0.7) 25 (111) 20.0 (89) -17.9 (-80) 17.5 (78) 17.1 (76) 1.12 1.02
16 94 (0.7) 25 (111) 24.0 (107) 18.7 (83) 21.8 (97) 19.0 (84) 1.28 1.15
Mean 1.15
COV (%) 6.5
The predictions of Table A.8 can be repeated with the equivalent equation
in terms of compressive strength using Equation (A.12). The resulting average
ratio of observed Vflcr to predicted Vflcr is 1.1, with a COV of 14%.
The formation of flexural cracks did not cause a decrease in strength or
stiffness of the specimens. Examples of the hysteretic behavior are shown in
Figure A.8 through Figure A.12. In each case at least one load cycle was
completed before a significant loss of stiffness was observed. Furthermore, the
vertical reinforcement was sufficient to carry the load after flexure-shear cracking
occurred. Based on these conclusions, no limiting design equations are proposed
for flexure-shear cracking.
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-15
-10
-5
0
5
10
15
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Drift Ratio (%)-66
-44
-22
0
22
44
66
before flexural crack
before propagation
after propagation
Figure A.8 Hysteretic behavior of Shear Wall Specimen 13 before and after
flexure-shear cracking
-15
-10
-5
0
5
10
15
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Drift Ratio (%)
-66
-44
-22
0
22
44
66
before flexuralcrackbefore propagation
after propagation
Figure A.9 Hysteretic behavior of Shear Wall Specimen 14b before and after
flexure-shear cracking
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-30
-20
-10
0
10
20
30
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Drift Ratio (%)
-133
-89
-45
0
44
89
133
before flexural crack
before diagonal crack
after propagation
Figure A.10 Hysteretic behavior of Shear Wall Specimen 15a before and after
flexure-shear cracking
-40
-30
-20
-10
0
10
20
30
40
-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6
Drift Ratio (%)
Bas
e Sh
ear (
kips
)
-178
-134
-89
-45
0
44
89
133
178
Bas
e Sh
ear (
kN)
before flexure-shear cracking south
before flexure-shear cracking north
after flexure-shear cracking
Figure A.11 Hysteretic behavior of Shear Wall Specimen 15b before and after
flexure-shear cracking
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155
-30
-20
-10
0
10
20
30
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Drift Ratio (%)
Bas
e Sh
ear (
kips
)
-133
-89
-45
0
44
89
133
Bas
e Sh
ear (
kN)
before flexure-shear cracking south
before flexure-shear cracking north
after flexure-shear cracking
Figure A.12 Hysteretic behavior of Shear Wall Specimen 16 before and after
flexure-shear cracking
A.1.3 Crushing of the Diagonal Strut
An AAC shear wall can transfer load through the formation of a diagonal
strut. The resultant of the applied lateral load and vertical forces acting on a wall
is transferred along a diagonal strip in the wall (Figure A.13). The compressive
force transferred along the diagonal strut is equilibrated at the base of the wall by
the frictional resistance and by the vertical component of the compressive force in
the diagonal strut. AAC shear walls with high axial loads can fail by crushing of
this diagonal strut.
Crushing of the diagonal strut will occur in an AAC shear wall when the
compressive stress in the strut exceeds the compressive strength of the AAC.
Figure A.14 shows the external forces acting on an AAC shear wall due to in-
plane shear and axial load.
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Vertical tie down forcesApplied
lateral load
Frictional forces
Compressive force in diagonal strut
Vertical tie down forcesApplied
lateral load
Frictional forces
Compressive force in diagonal strut
Figure A.13 Diagonal compressive strut in an AAC shear wall
V
Tr3Tr2 Tr4
Tr1
V
Tr3Tr2 Tr4
Tr1
Figure A.14 External forces acting on an AAC shear wall
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Diagonal crushing can be predicted using a strut-and-tie model consisting
of two elements: a diagonal compression strut (Fstrut); and a tension tie-down
force (T). The compressive force in the diagonal strut is the resultant of the
vertical tie-down forces and the applied horizontal load. Because the system is
statically determinate, the vertical component is the summation of the force in the
tie-down rods, and the horizontal component is the applied lateral load (V).
Force in Diagonal str )
w
Friction Force
Compressive Stressin Diagonal
Summation of Vertical Tie Down Forces
Applied HorizontalLoad
w
Strut FForce in Diagonal Strut F strut
wstrut
Friction
Compressive Stressin Diagonal Strut
Applied HorizontalLoad (V)
w
Summation of Vertical Tie-Down Forces
Force in Diagonal str )
w
Friction Force
Compressive Stressin Diagonal
Summation of Vertical Tie Down Forces
Applied HorizontalLoad
w
Strut FForce in Diagonal Strut F strut
wstrut
Friction
Compressive Stressin Diagonal Strut
Applied HorizontalLoad (V)
w
Summation of Vertical Tie-Down Forces
Figure A.15 Forces acting on diagonal strut in an AAC shear wall
Equation (A.19) represents the horizontal force (V) at crushing based on
equilibrium of horizontal forces at the base of the diagonal strut. The derivation
can be shown in Equation (A.13) to Equation (A.18). The limiting force in the
diagonal strut is based on an uniform compressive stress acting over the smallest
area of the strut, as shown in Equation (A.13). The maximum applied lateral load
is related by geometry to the force in the strut. Likewise, the minimum width of
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the strut can be related to the horizontal width of the diagonal strut. By
substitution, the lateral load of Equation (A.19) can be expressed in terms of the
wall geometry and horizontal width of the strut (see Equation (A.16) and
Equation (A.17)).
AACstrut wtfF = Equation (A.13)
)cos(θstrutds FV = Equation (A.14)
strutww )sin(θ= Equation (A.15)
( )[ ] 5.022)cos(
strutw
strutw
wlh
wl
−+
−=θ ,
( )[ ] 5.022)sin(
strutw wlh
h
−+=θ
Equation (A.16)
Equation (A.17)
)sin()cos( θθAACstrutds ftwV ⋅⋅= Equation (A.18)
( )( )[ ]
−+
−⋅⋅⋅=
22strutw
strutwstrutAACds
wlh
wlhwtfV Equation (A.19)
Shear Wall Specimen 1 (UT Austin) confirmed this proposed model for
crushing of the diagonal strut. Minor spalling occurred at the toe at a load of 152
kips (676 kN), and major spalling, at a load of 167.6 kips (745 kN). The observed
horizontal width of the diagonal strut was approximately one-quarter of the plan
length. Using Equation (A.19), crushing of the diagonal strut for Shear Wall
Specimen 1 was predicted at a lateral load of 185.1 kips (823 kN). The ultimate
load was 90% of the load predicted by the model for crushing of the diagonal
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159
strut. Since, the model for crushing of the diagonal strut was unconservative in
this case, it is multiplied by a factor of 0.9. Equation (A.20) incorporates this
factor and a width of the compression strut of 0.25lw. The results of the predicted
lateral load at crushing of the diagonal strut, for an assumed strut width of one-
quarter of the plan length, are presented along with the ultimate lateral load in
Table A.9.
2432
2
)(17.0
w
wAACAAC lh
lhfV+
⋅⋅= Equation (A.20)
Table A.9 Predicted shear wall capacities as governed by crushing of the
diagonal strut
Specimen
Vds kips (kN)
0.9Vds kips (kN)
Maximum V kips (kN)
0.9 Vds – Maximum V
Maximum V
/ 0.9 Vds 1 185 (824) 167 (741) 168 (745) -1 (-4) 1.01 3 154 (683) 138 (615) 118 (526) 20 (89) 0.86 4 315 (1403) 284 (1262) 126 (561) 158 (701) 0.44 5 246 (1093) 221 (984) 85 (377) 136 (607) 0.38 7 89 (394) 80 (355) 59 (263) 21 (91) 0.74 9 98 (436) 88 (392) 42 (189) 46 (204) 0.48
11 23 (100) 20 (90) 17 (74) 4 (16) 0.82 13 21 (93) 19 (84) 22.5 (100) -4 (-16) 1.19 14a 36 (162) 33 (146) 9.9 (44) 23 (102) 0.30 14b 36 (162) 33 (146) 10.1 (45) 23 (101) 0.31 15a 121 (537) 109 (483) 30.1 (134) 79 (350) 0.28 15b 121 (537) 109 (483) 30.9 (137) 78 (346) 0.28 16 121 (537) 109 (483) 35.2 (157) 73 (327) 0.32
In the remaining shear wall specimens crushing of the diagonal strut was
avoided by limiting the axial load. The validity of Equation (A.20) was indirectly
determined by avoiding crushing. In Shear Wall Specimen 13, the maximum
lateral load was higher than the proposed equation for the design provisions
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without observing crushing of a diagonal strut. One reason for the discrepancy is
that the assumed width of the diagonal strut of one-quarter of the plan length of
the wall is no longer valid. The aspect ratio of Shear Wall Specimen 13 is 2.
Since the model was adequate for walls with aspect ratios less than 2, that aspect
ratio is used as an upper limit to the proposed Code equation.
A.1.4 Sliding Shear Capacity
An AAC shear wall of horizontal panels or masonry-type blocks exhibits a
bed-joint crack when the shear stress on the bed joints exceeds the interface shear
capacity, ν (Figure A.18 ). An AAC shear wall subject to sliding shear across a
horizontal bed joint is presented in (Figure A.16). After the crack forms the shear
is resisted by the vertical reinforcement and frictional forces due to the axial load.
VN
Figure A.16 Formation of bed-joint crack in an AAC shear wall with horizontal
panels
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161
VN
Figure A.17 Sliding shear mechanism in an AAC shear wall with horizontal
panels
After the crack forms, some resistance will be provided by shear friction
across the bed joints:
( )ΝfΑµV svss += Equation (A.21)
Sliding shear resistance is the product of the coefficient of friction across
an interface, and the force acting perpendicular to that interface. This mechanism
is referred to in ACI 318 as “shear friction.” This resistance can come from
reinforcement crossing the interface and applied axial load.
In the traditional “shear friction” mechanism, sliding over a rough joint
causes one section of the crack to lift upwards; this result in yielding of the
vertical reinforcement, which provides additional clamping force. Under reversed
cyclic loading of AAC, the roughness of the bed joints can decrease, and
resistance to sliding shear is provided by dowel action of reinforcement crossing
the bed joints. This contribution to Vss is the area of the reinforcement
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perpendicular to the crack and the shear resistance of the bars, 0.6fy. This
contribution to the sliding shear mechanism is shown in Figure A.18.
V
Av0.6fy Av0.6fy Av0.6fyAv0.6fy Av0.6fy
V
Av0.6fy Av0.6fy Av0.6fyAv0.6fy Av0.6fy Figure A.18 Internal lateral forces generated by dowel action along plane of
sliding shear mechanism
Frictional resistance is the second component of resistance due to sliding
shear. Figure A.19 is a free-body diagram showing the horizontal equilibrium due
to frictional forces.
V
N
µN
0.25N 0.25N 0.25N 0.25N
V
N
µN
0.25N 0.25N 0.25N 0.25N
Figure A.19 Internal lateral forces generated by friction along plane of sliding
for sliding shear mechanism
ysss f0.6ANV += µ Equation (A.22)
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In subsequent specimens, the clamping force N was determined such that
the shear capacity will be limited by web-shear cracking or flexure-shear
cracking, rather than bed-joint sliding. Sliding shear was avoided in 12 out of the
remaining 14 specimens; it was observed in Shear Wall Specimen 4 and the Two-
story Assemblage Specimen. Since the specimens were designed to avoid sliding
shear, sufficient dowels were placed to ensure that Vss was significantly greater
the VAAC. In four specimens, Vmax was greater than VAAC. Shear Wall Specimen 3
and Shear Wall Specimen 5 were both overdesigned in sliding shear. The load
did not reach the sliding shear capacity because the specimen capacities were
limited by distributed web-shear cracking. Shear Wall Specimen 4 and the Two-
story Assemblage Specimen can be used to determine the effectiveness of
Equation (A.22).
The hysteretic behavior for the Two-story Assemblage Specimen is shown
in Figure A.20. The total base shear and sliding shear capacity for the specimen
versus Load Point is presented in Figure A.21. The design sliding shear capacity
is presented for the contribution of axial load and dowels (Equation (A.22)) and
the contribution of axial load only. A coefficient of friction of 1.0 was used since
the sliding plane occurred between the vertical panels and the leveling bed mortar.
The entire axial load was applied through gravity, therefore, the axial load
remained constant throughout the test. In this specimen the longitudinal steel and
dowels contribute significantly to the capacity for several cycles. Damage around
the dowels began at Load Point 677 and continued throughout the test. Each
loading cycle was accompanied by increasing damage. The cumulative damage at
each cycle is accompanied by a continually decreasing base shear, as shown in
load points above 800 in Figure A.21.
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-160
-120
-80
-40
0
40
80
120
160
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Average drift ratio in %
Tota
l bas
e sh
ear (
kips
)
-712
-534
-356
-178
0
178
356
534
712
Tota
l bas
e sh
ear (
kN)
Figure A.20 Hysteretic behavior of Two-story Assemblage Specimen
0
20
40
60
80
100
120
140
160
0 100 200 300 400 500 600 700 800 900 1000 1100
Load Point
Bas
e Sh
ear (
kips
)
0
89
178
267
356
445
534
623
712
Bas
e Sh
ear (
kN)
Capacity with axial load onlyCOF=1
Base shear on system
Design capacity with axial loadand dowels
Figure A.21 Base shear and sliding shear capacity versus Load Point for Two-
story Assemblage Specimen
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Sliding was observed in two adjacent panels in Shear Wall Specimen 4. A
horizontal crack formed along the bed joint between the second and third courses.
This crack formed in three stages, corresponding to Load Points 634, 717 and
764. The final crack propagation occurred after the maximum base shear was
reached. A graph of base shear versus Load Point for Shear Wall Specimen 4 is
shown in Figure A.22. Since the sliding occurred between panels, a coefficient of
friction of 0.8 was used to predict the capacity. The applied base shear increased
beyond the sliding shear resistance for the level of axial load that was applied to
the specimen. Several diagonal cracks formed at the compression toes of the
walls. Spalling between these cracks occurred at Load Point 871.
The axial load consisted of three portions: gravity load from loading
equipment; load applied through the load maintainer; and post-tensioning force in
the rods. The pressure in the load maintainer system was checked during testing.
It did not change, nor did the contribution of axial load due to gravity. Any
decrease in axial load would therefore have to have occurred due to a loss of post-
tensioning. This was observed in the spalling of the compression toe that
occurred at Load Point 871. The loss of post-tensioning decreased the applied
axial load and thus decreased the sliding shear capacity.
The measured axial load capacity of Figure A.23 includes the unchanged axial
load and the measured force in the external rods. As the base shear increases, a
slight increase is also observed in the axial load (see Load Point 1080 through
1110). This is the increase in load in the axial rods caused by the in-plane
rotation of the wall about its compression toe. At later load points, at points of
zero base shear the force in the rods decreases due to toe crushing. This can be
observed in the difference between measured axial loads at two points where the
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base shear is zero. For example, at Load Point 830 the measured axial load is 91
kips (405 kN); at Load Point 890 it decreases to 87 kips (387 kN); and at Load
Point 960 it further decreases to 82 kips (365 kN).
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Drift Ratio (%)
Bas
e Sh
ear (
kips
)
-623
-534
-445
-356
-267
-178
-89
0
89
178
267
356
445
534
623
Bas
e Sh
ear (
kN)
f
Figure A.22 Hysteretic behavior of Shear Wall Specimen 4
For load points beyond 700 the base shear capacity decreases. This was
also observed in the Two-story Assemblage Specimen. This is a further
indication that as damage increases the effectiveness of the dowel action
decreases. As the damage increases, the resistance provided by bearing on the
dowel is reduced. For this reason, the proposed code language conservatively
neglects the contribution of the dowels as shown in Equation (A.23).
NVss µ= Equation (A.23)
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0
20
40
60
80
100
120
140
160
500 600 700 800 900 1000 1100 1200 1300 1400 1500
Load Point
Bas
e Sh
ear (
kips
)
0
89
178
267
356
445
534
623
712
Bas
e Sh
ear (
kN)
Capacity based on measured axial load COF=0.8
Capacity based on initial axial load COF=0.8
Base shear in wall
Capacity based on initial axial load and dowels
Figure A.23 Base shear and sliding shear capacity versus Load Point for Two-
Story AAC Assbemblage Specimen
Structures with small axial load may have low sliding shear capacity. In
these cases the interface shear strength between AAC and thin-bed mortar may be
used. Based on the direct shear tests performed at UT Austin, the average
interface shear strength between AAC and thin-bed mortar was 64 psi (441 kPa),
with a COV of 44%. A lower 5 % fractile is proposed, for design, reducing the
interface shear strength to 17 psi (117 kPa). This value is conservative compared
to test results of 45 psi (310 kPa) to 82 psi (565 kPa).
The measured axial load in Figure A.23 does not include the tensile forces
in the internal reinforcement. Although those forces were not measured, they can
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be estimated based on flexural calculations. The wall instrumentation indicates
that the longitudinal reinforcement in the wall had yielded at the bed joint where
sliding occurred. When the lateral load is removed and the bed-joint gap closes,
the bars will be subject to compression. Based on an assumed debonded bar
length, the compressive forces can be estimated. The solid blue line in Figure
A.24 shows the revised axial load considering compressive stresses in
longitudinal reinforcement.
0
20
40
60
80
100
120
140
500 600 700 800 900 1000 1100 1200 1300 1400 1500
Load Point
Bas
e Sh
ear (
kips
)
0
89
178
267
356
445
534
623
712
Bas
e Sh
ear (
kN)
Capacity based on measured axial load COF=0.75
Capacity based on initial axial load COF=0.75
Base shear in wall
Capacity based on measured axial load andcalculated residual compressive forces COF=0.75
Figure A.24 Base shear and reduced sliding shear capacity versus Load Point
for Two-story Assemblage Specimen
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A.1.5 Nominal Flexural Capacity
The nominal flexural capacity of AAC shear walls can be determined
based on equilibrium of a cross section. Using the proposed design provisions,
the nominal flexural capacity of AAC shear walls can be predicted using
conventional flexural theory. The compressive zone is determined based on a
linear strain relationship, using a maximum useful compressive strain in the AAC
of 0.003 (RILEM 1993 and Section 4.3.1), and an equivalent rectangular stress
block whose height is 0.85f ′AAC (or 0.85f ′m), and whose depth is β1c, where β1 =
0.67 (Figure A.25). The value of β1 is selected to maintain equilibrium between
the equivalent stress block and a triangular compressive stress distribution based
on tested stress-strain results of Section 3.6.1.
cP
V
AsFs β1c
0.85 f ′AACAsFs
cV
AsFsAsFs β1c
0.85 f ′AACAsFsAsFs
cP
V
AsFsAsFs β1c
0.85 f ′AACAsFsAsFs
cV
AsFsAsFs β1c
0.85 f ′AACAsFsAsFs
Figure A.25 Equilibrium of an AAC shear wall at nominal flexural capacity
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Observed versus predicted nominal flexural capacities can be compared
for flexure-dominated Shear Wall Specimen 14a, 14b, 15a and 15b. During the
test of Shear Wall Specimen 13 and Shear Wall Specimen 16, the actuators used
to apply the constant axial load inadvertently reached the end of their travel. As
increasing lateral drifts were applied, axial load on the wall inadvertently
increased. To successfully interpret those test results, the probable axial load
applied to the walls was back-calculated from the predicted flexural capacity,
removing those two tests from consideration for verifying observed versus
predicted flexural capacity.
The nominal flexural capacity was calculated using a steel yield strength
of 75 ksi (490 MPa), based on mill reports, along with the assumptions of 8.8.2.
The ratios of observed to predicted strength range from 1.11 to 1.29, with an
average of 1.19 and a COV of 5.8%. A refined analysis was performed
considering strain hardening using RCCOLA (RCCOLA). The effect of strain
hardening will increase the nominal flexural capacity as shown in the results of
Table A.11. With this refinement the range of observed to predicted nominal
flexural capacity ranges from 0.95 to 1.13. The average is 1.03 with a COV of
6.2%.
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Table A.10 Observed versus predicted nominal shear capacities based on
nominal flexural capacity
Specimen Predicted VMn
kips (kN)
Observed VMn South kips (kN)
Observed VMn Northkips (kN)
Observed / Predicted VMn South
Observed / Predicted VMn
North
14a 8.5 (38) 9.4 (42) NA 1.11 NA
14b 8.5 (38) 9.9 (44) 10.1 (45) 1.16 1.19
15a 23.9 (106) 28.8 (128) 30.1 (134) 1.21 1.26
15b 23.9 (106) 26.7 (119) 30.9 (137) 1.12 1.29
Average 1.19
COV (%) 5.8
Table A.11 Observed versus predicted nominal shear capacities based on
nominal flexural capacity with strain hardening included
Specimen Predicted VMn
kips (kN)
Observed VMnSouth
kips (kN)
Observed VMn North kips (kN)
Observed / Predicted VMn South
Observed / Predicted VMn
North
14a 9.9 (44) 9.4 (42) NA 0.95 NA
14b 9.9 (44) 9.9 (44) 10.1 (45) 1.00 1.02
15a 27.4 (122) 28.8 (128) 30.1 (134) 1.05 1.10
15b 27.4 (122) 26.7 (119) 30.9 (137) 0.97 1.13
Average 1.03
COV (%) 6.2
A.2 SPECIAL PROVISIONS FOR VERTICAL PANEL CONSTRUCTION
AAC panels oriented vertically have potential planes of failure along
continuous head joints. These cracks may be attributed to shrinkage or weak
joints, where the thin-bed mortar is not in contact with both panel faces. The
presence of vertical cracks can change the behavior of a shear wall specimen.
The observance of this behavior in Shear Wall Specimen 2 will be discussed then
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172
theoretical and design methodologies will be presented in Sections A.2.1 and
A.2.2.
In Shear Wall Specimen 2, two vertical cracks formed prior to testing.
Shortly after flexural cracks formed another two vertical cracks formed and
separated the wall into smaller sections. The initial cracks are indicated by gray
lines and the cracks formed during testing are indicated by black lines in Figure
A.26. The first diagonal crack formed at a load of 55.6 kips (247 kN). As the
load increased, additional vertical and diagonal cracks formed in the specimen
(Figure A.27).
Figure A.26 Formation of first diagonal crack in Shear Wall Specimen 2
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Figure A.27 Formation of additional cracks in Shear Wall Specimen 2
A.2.1 Prediction of Flexural and Shear Capacities for AAC Shear Walls
with Vertically Oriented Panels
In the case of monolithic behavior, the wall behaves as a cantilever (see
Figure A.28). In the case of individual panels, the stiffness of the loading beam is
large compared to a single panel, and the loading beam restrains the wall at the
top (Figure A.29). If the wall behaves monolithically, the shear capacity will
remain the same as presented in Section A.1, and the flexural design will be
conventional. If the panels are separated by vertical cracks at the head joints,
however, the behavior will change. That is the subject of this section.
.
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L
Figure A.28 Behavior of monolithic AAC shear wall
L
L 2
Figure A.29 Behavior of individual panel for an AAC shear wall
The most critical case would be panels with vertical cracks at every
section. The flexural capacity can be predicted based on the sum of the capacity
of the individual panels. An interaction diagram for a single panel can be
calculated and the flexural capacity of each panel can be determined based on the
axial load in the respective panel; a value that depends on the forces acting on the
wall. The lateral load will produce a series of axial loads in each panel that vary
linearly based on the wall geometry. The applied axial load per panel will be the
total axial load divided by the number of panels (see Figure A.30).
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Figure A.30 Distribution of axial loads for laterally loaded condition and
axially loaded condition
If the net axial load applied to each panel is within the straight-line portion
of the interaction diagram for a single panel, the total wall capacity will be the
capacity at the axial load in a single panel, multiplied by the number of panels:
panelswall VV Σ= Equation (A.24)
panelswall MM Σ= Equation (A.25)
If the wall behaves as individual panels, the aspect ratio of piece becomes
large; each panel behaves as a beam subject to compressive and lateral loads. The
shear capacity in this condition can be predicted using the shear equations for
beams presented in Section 4.5.
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A.2.2 Verification of Shear Capacity for Vertical-Panel Shear Walls Tested
at UT Austin
The application of the individual panel design equations and the
monolithic wall equations for Shear Wall Specimen 2 is presented in Figure A.31.
The base shear at which cracking occurred was 55 kips (245 kN), and the
maximum base shear was 92 kips (410 kN). The design equations are much more
conservative than the wall behavior.
Several conditions can increase the performance of a head joint between
vertical panels:
a) Cleaning and wetting the panel face prior to application of the thin-bed
mortar improves the adhesion.
b) Applying mortar to both faces of the vertical joint improves the mortar
coverage at the joint.
c) Clamping adjacent panels applies pressure and improves the joint quality.
In Shear Wall Specimen 2 the panel faces were prepared and pressure was
applied perpendicular to the joint, parallel to the plane of the wall. Initially, the
joints were not mortared on both faces. After a lack of coverage was observed in
several joints, the panel was removed, cleaned and re-installed with mortar
applied to both faces of the joint. This procedure was applied thereafter. The
joint was clamped at the base (using one clamp on each wall face) and at the top
(using one clamp at the centerline of the wall).
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In the remaining specimens constructed of vertical panels (Shear Wall
Specimens 15, 16 and the Two-story Assemblage Specimen), vertical cracks were
not observed. In each case the three previous construction recommendations were
used. Pressure was applied to the joint using 4 clamps, one clamp on each wall
face, both at the bottom and top of the wall.
0
200
400
600
800
1000
0 50 100 150 200 250
Base Shear (kips)
Axi
al F
orce
(kip
s)
0.0
0.9
1.8
2.7
3.6
4.40 222 445 667 890 1112
Base Shear (kN)
Axi
al F
orce
(MN
)
ShearCapacityMonolithicWall
Flexural CapacityMonolithic Wall
Flexural CapacityΣ Individual Panels
Shear CapacityΣ Individual Panels
Base shear at cracking
Shear Capacity of wall
Figure A.31 Base shear capacity for Shear Wall Specimen 2 considering
individual panel behavior and monolithic wall behavior
In these specimens, vertical cracks at the joints were not observed until the
end of the test when the wall stiffness was reduced due to prior cracks.
Furthermore, the cracks left at least three panels joined together. For this
construction type, the proposed design recommendation is to relax the individual
panel requirements to groups of three panels connected together. The changes to
the flexure and shear design capacities are presented in Figure A.32. Equation
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(A.3) to predict web-shear cracking was used for panel groups with an aspect ratio
less than 2.
0
200
400
600
800
1000
0 50 100 150 200 250
Base Shear (kips)
Axi
al F
orce
(kip
s)
0.0
0.9
1.8
2.7
3.6
4.40 222 445 667 890 1112
Base Shear (kN)
Axi
al F
orce
(MN
)
ShearCapacityMonolithicWall
Flexural CapacityMonolithic Wall
Flexural CapacityΣ Individual Panels
Shear CapacityΣ Individual Panels
Flexural CapacityΣ Panel Groups
Base shear at cracking
Shear capacity of wall
Shear CapacityΣ Panel Groups
Figure A.32 Base shear capacity for Shear Wall Specimen 2 considering
individual panel behavior, behavior of panel groups and monolithic wall
behavior
A.2.3 Special Provisions to Avoid Longitudinal Cracking at the Location of
Vertical Reinforcement
In each of the flexure-dominated specimens vertical (longitudinal) cracks
formed along the grouted cores and the surrounding AAC. In the following
sections the observed load at which these cracks formed is presented, along with
two analyses to determine if the cracks occurred before yielding of the flexural
reinforcement. The effect of these longitudinal cracks is presented, followed by
design recommendations intended to prevent their formation.
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A.2.4 Formation of Cracks along Longitudinal Bars in AAC Shear Walls
The base shears at which cracks formed along longitudinal reinforcement
formed are presented in Table A.12. The base shear at which the first and second
cracks formed along the vertical reinforcement is presented in Column 2 of that
table. No second observed vertical crack data are presented for Shear Wall
Specimen 14a, because that wall was tested in one direction only. The base shear
at the expected flexural capacity (nominal capacity increased by steel
overstrength) is presented in Column 3.
Table A.12 Ratio of base shear at formation of vertical cracks to base shear at
expected flexural capacity (including overstrength) in the flexure-dominated
shear wall specimens
AAC Shear Wall Specimen
Base shear at first and second observed vertical
crack, kips (kN)
Base shear at expected flexural capacity (fs=1.25fy) Vmax
kips (kN)
Ratio of base shear at observed crack to Vmax
(fs=1.25fy)
13 13.6 (60) – first
15.6 (69) - second 13.0 (58) 1.05 – first
1.20 – second
14a 6.9 (31) – first NA – second 8.3 (37)
0.83 – first NA – second
14b 7.0 (31) – first
9.8 (44) - second 8.3 (37) 0.84 – first
1.18 – second
15a 26.5 (118) – first
27.3 (128) - second 23.8 (106) 1.11 – first
1.15 – second
15b 17.5 (78) – first
24.5 (109) - second 23.8 (106) 0.74 – first
1.03 – second
16 24.0 (107)– first
28.0 (125) - second 25.5 (113) 0.94 – first
1.10 – second
The ratios of base shear at the observed crack to the base shear at the
expected flexural capacity range from 0.74 to 1.20, with an average of 1.02 and a
COV of 16%. Longitudinal cracks were observed in three specimens at 74% to
84% of the expected flexural capacity. The ratios of base shear at cracking to
expected flexural capacity, along with a corresponding normal distribution, are
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shown in Figure A.33. As shown in that figure, it is highly probable that an AAC
shear wall will reach between 74% and 84% of its expected flexural capacity in a
moderate to strong earthquake, and therefore highly probable that such
longitudinal cracks would form.
0.8
1
1 .2
1 .4
1 .6
0.25 0.50 0.75 1.00 1.25 1.50 1.75Load at vertical crack / Expected flexural capacity (1.25 fy)
Data points
Normaldistributioncurve
Figure A.33 Ratio of base shear at observed longitudinal crack to base shear at
expected flexural capacity (fs=1.25 fy)
For lower base shears, a similar analysis can be performed. The results of
Table A.12 are reproduced based on nominal moment capacity (rather than
expected), and are presented in Table A.13. In this case the ratios of base shear at
longitudinal cracking to base shear at nominal capacity range from 0.84 to 1.42,
with an average of 1.2 and a COV of 15.5%. These data are illustrated
graphically in Figure A.34. The ratio of 1.0 between base shear at longitudinal
cracking to base shear at nominal flexural capacity, corresponds to a 16% lower
fractile. A 5% lower fractile corresponds to a ratio of 0.88. Based on these
results, 5% of shear walls would exhibit longitudinal cracking at the factored
nominal flexural capacity. To further determine if vertical cracks would occur at
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service loads, analyses were performed to determine if the cracks formed prior to
yielding, and are presented in the following section.
Table A.13 Ratio of base shear at observed vertical cracking to the nominal
flexural capacity (without overstrength) in flexure-dominated AAC shear wall
specimens
Specimen
Base shear at first and second observed vertical
crack kips (kN)
Base shear at design flexural capacity VMn
kips (kN)
Ratio of base shear at first observed
crack to VMn
13 13.6 (60) – first
15.6 (69) - second 11.4 (51) 1.19 – first
1.37 – second
14a 6.9 (31) – first NA – second 6.9 (31)
1.00 – first NA – second
14b 7.0 (31) – first
9.8 (44) - second 6.9 (31) 1.01 – first
1.41 – second
15a 26.5 (118) – first
27.3 (128) - second 20.9 (93) 1.27 – first
1.31 – second
15b 17.5 (78) – first
24.5 (109) - second 20.9 (93) 0.84 – first
1.17 – second
16 24.0 (107) – first
28.0 (125) - second 22.2 (99) 1.08– first
1.26 – second
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0.8
1
1 .2
1 .4
0.25 0.50 0.75 1.00 1.25 1.50 1.75
Load at vertical crack / Design flexural capacity
Data points
Normal distributioncurve5% Lower fractile
16% Lower fractile
Figure A.34 Ratio of base shear at observed longitudinal crack to base shear at
nominal flexural capacity without overstrength
A.2.5 Analysis to Determine if Longitudinal Cracks Formed Prior to
Yielding
Additional analysis was performed to determine if longitudinal cracks
formed before or after the vertical reinforcement yielded. If the vertical cracks
formed prior to yielding, then those cracks might also be present in walls at
factored design loads. If the vertical cracks formed after yielding, it can be
assumed that they would occur only during overloading beyond the nominal
capacity.
Strain was measured by three strain gages on the longitudinal
reinforcement at each end of the wall. If one strain gage indicated strains beyond
yield and another strain gage indicated strains near but not exceeding yield, this
was assumed to denote yielding. The base shear and load points at the formation
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of longitudinal cracks in each specimen, while loading to the south and to the
north, are recorded in Column 2 of Table A.14. In Shear Wall Specimen 13,
strain gage data were not available; for this reason, in Column 2 both the South
and North loading directions are labeled “NA.” The base shear and load points at
the yielding of the flexural reinforcement are presented in Column 3. Since load
points are assigned in ascending order, the first event (either longitudinal cracking
or yielding of longitudinal reinforcement) has the lowest-numbered load point.
The event that occurred first for each loading direction is presented in Column 4.
If the load-point numbers did not vary by more than 5, it was assumed that
longitudinal cracking occurred simultaneously with yielding of flexural
reinforcement, and was therefore associated with that yielding. For example, in
Shear Wall Specimen 14a while loading to the south, longitudinal cracking was
observed at Load Point 542, and the longitudinal reinforcement was determined to
have yielded at Load Point 539. Since these load points do not vary by more than
5, it was concluded that the longitudinal cracking and yielding of the
reinforcement occurred simultaneously, as indicated in Column 4. Finally, the
ratio of base shear at longitudinal cracking to base shear at yielding is presented in
Column 5.
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Table A.14 Estimation of order of vertical cracking and yielding of longitudinal
reinforcement, based on strain gages
Specimen
Base shear at observed vertical crack, loading
south and loading north,
Kips (kN) Load point
Base shear at yielding of flexural reinforcement,
loading south and loading north, kips (kN)
Load point
Estimated order of yielding of
reinforcement and longitudinal
cracking
Ratio of base shear at formation of
longitudinal crack of base shear at
yielding of flexural reinforcement
13 13.6 (60) LP 1023 – S 15.6 (69) LP 1232 - N
NA – S NA – N
NA – S NA – N
NA – S NA – N
14a 6.9 (31) LP 542 – S
NA – N 6.2 (27.6) LP 539 – S
NA – N Together – S
NA – N 1.1 – S NA – N
14b 7.0 (31) LP 326 – S 9.8 (25) LP 487 - N
7.5 (33) LP 327 – S 8.9 (40) LP 410 – N
Together – S Yielding – N
0.9 – S 1.1 – N
15a 28.8 (128) LP 437 – S 27.3 (121) LP 528 – N
22.1 (98) LP 299 – S 26.0 (116) LP 333 – N
Yielding – S Yielding – N
1.3 – S 1.1 – N
15b 17.5 (78) LP 202 – S
24.5 (109) LP 338 – N 23.7 (102) LP 363 – S 24.5 (109) LP 340 – N
Cracking – S Together – N
0.7 – S 1.0 – N
16 28.0 (125) LP 716 – S 24.0 (107) LP 426 - N
27.0 (120) LP 704 – S 26.8 (119) LP 754 – N
Yielding – S Cracking – N
1.0 – S 0.9 – N
In four cases, yielding occurred before longitudinal cracking; and in two
cases, it occurred afterwards. In the remaining cases these events probably
occurred simultaneously. In both cases where the flexural reinforcement yielded
after longitudinal cracks were observed, the ratio of base shear at formation of
longitudinal cracking to base shear at yielding was also less than 1. This further
supports the conclusion that if #5 bars are used in 3-in. grouted cores, longitudinal
cracks may form prior to yielding of the flexural reinforcement. The ratio of base
shear at longitudinal cracking to base shear at yielding is less than 1.25 for all of
the specimens, which indicates that longitudinal cracks will probably form prior
to reaching the nominal flexural capacity considering a strain hardening factor of
1.25. This analysis does not consider the height at which the vertical crack
formed. If the crack formed at a height of 48 in. (1.2 m) the stress in the
reinforcement could be significantly below yield. The impact of crack height is
considered in a separate analysis.
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An additional analysis was performed to estimate the stress in the flexural
reinforcement at longitudinal cracking, using elastic flexural stresses calculated
based on a cracked transformed section (Table A.15). The applied base shear was
converted to an applied moment at the location of the crack by multiplying by the
height of the wall minus the crack height. The stress in the longitudinal tensile
reinforcement was computed using Equation (A.26). The contributions from the
axial load are not presented in Table A.15 because they were less than 2 ksi (14
MPa). The distance from the neutral axis to the centroid of the tensile
reinforcement is denoted by yAs; the modular ratio between steel and AAC is
denoted by n; and the cracked transformed moment of inertia is denoted by Icrtr.
The results indicate that in 6 of the 11 cases, calculated stresses at longitudinal
cracking exceeded the expected yield strength of 75 ksi (10.9 GPa). This
indicates that approximately half of the vertical cracks occurred prior to or
simultaneously with yielding of the flexural reinforcement.
trcrtr
AsAs A
PnI
nMy−=σ Equation (A.26)
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Table A.15 Calculated stresses in tensile reinforcement based on elastic theory
for vertical cracks on the south and north sides of the specimen
Specimen
Base shear at observed vertical
crack, loading south and loading
north kips (kN)
Height of the vertical
crack in. (m)
Cracked transformed moment of
inertia in.4 (m4)
yAs, distance from the area of tensile steel to the
neutral axis in. (m)
Calculated stress in tensile reinforcement
for first observed vertical crack
ksi (GPa)
13 13.6 (60) – S 15.6 (69) – N
24 (0.6) – S24 (0.6) – N 64900 (0.027) 45 (1.1)
96 (0.67) – S 111 (0.79) – N
14a 6.9 (31) – S
NA – N 48 (1.2) – S
NA – N 46100 (0.019) 39 (1.0) 49 (0.35) – S
NA – N
14b 7.0 (31) – S 9.8 (44) – N
24 (0.6) – S48 (1.2) – N 46100 (0.019) 39 (1.0)
61 (0.44) – S 70 (0.50) – N
15a 28.8 (128) – S 27.3 (121) – N
48 (1.2) – S0 (0) – N 226800 (0.094) 86 (2.2)
91 (0.65) – S 127 (0.90) – N
15b 17.5 (78) – S
24.5 (109) – N 12 (0.3) – S24 (0.6) – N 226800 (0.094) 86 (2.2)
74 (0.53) – S 95 (0.68) – N
16 28.0 (125) – S 24.0 (107) – N
0 (0) – S 24 (0.6) – N 309100 (0.129) 94 (2.4)
104 (0.73) – S 75 (0.54) - N
A.2.6 Implications of the Formation of Longitudinal Cracks
The above evaluations show that longitudinal cracks are highly probable
in real AAC shear walls subject to lateral loads. This section is devoted to
explaining the probable consequences of those cracks and providing design
recommendations for preventing them.
Cracks along reinforcement in a grouted core are inherently undesirable,
because they provide an opportunity for air and water to enter the core, and
thereby increase the probability of corrosion of that reinforcement. Longitudinal
cracks along the height of the wall, combined with horizontal cracks, can cause
the end blocks to spall and crush sooner than in otherwise identical walls without
longitudinal cracks (Figure A.35). Longitudinal cracks can also lead to buckling
of the longitudinal reinforcement in the compression toe (Figure A.36).
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Figure A.35 Loss of end block on compression toe in Shear Wall Specimen 16
Figure A.36 Loss of end blocks and buckling of compression reinforcement in
Shear Wall Specimen 15b
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188
As the load is reversed, the previously buckled longitudinal reinforcement
may fracture, effectively reducing the wall’s flexural capacity to zero. Examples
of the undesirable consequences of loss of the compression toe are shown by
Shear Wall Specimen 15b and Shear Wall Specimen 16.
Resistance to cracks along longitudinal reinforcement could be increased.
Longitudinal splitting cracks could be prevented by increasing the size of grouted
core or decreasing the bar diameter. This is equivalent to limiting the ratio of area
of the longitudinal reinforcement to area of core (area ratio).
The area ratio of a #5 (17 mm) bar in a 3-in. (76 mm) diameter grouted
core (4.4%) was observed to produce splitting along longitudinal bars in plastic
hinge zones. This is inherently undesirable for AAC shear walls. Such cracking
not been observed with #4 bars in 3-in. grouted cores, even at splices. A #4 (12
mm) bar in a 3 in. (76 mm) core corresponds to an area ratio of 2.8%. For that
reason, the proposed design provisions for AAC masonry and reinforced AAC
panels limit the maximum ratio of the area of reinforcement to the area of the
grouted core containing that reinforcement, to 3% in plastic hinge zones.
A.2.7 Analysis of Maximum Permissible Area Ratio if Longitudinal
Reinforcement Remains Elastic
Area ratios of reinforcement up to 4.5% are permitted, provided that radial
(splitting) stresses can be limited by limiting the bond stress, which in turn means
limiting the shear. The formation of radial stresses is explained in Section 8.8 of
this dissertation, and briefly reviewed here.
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189
After the initial adhesion between the reinforcement and concrete is
broken, load is transferred from deformed reinforcement to the surrounding
concrete or grout by the deformations (lugs). The axial component of the force
transferred by the lugs to a vertical core is the difference in force (∆T) in a section
of vertical reinforcement (Figure A.37). The associated radial component of that
force also acts on the surrounding grout (Figure A.37). The resultant forces
generally act at about 45 degrees to the axis of the reinforcement, so that the
resultants of the radial and axial component of the forces are equal. The radial
forces generated per length of the bar equal the change in force in the bar over
that same length. The pressure generated by the radial forces in the longitudinal
bar can be determined by dividing the radial forces by the product of the
circumference of the deformed bar and the length of the section of the bar, ∆x, as
shown in Figure A.37. The diameter of the longitudinal bar is denoted by dbar.
T + ∆T
T
Lugs
Forces transferred to bar at the lugs
∆x
Axial cross-section of lug on reinforcement showing radial forces on grout surrounding the bar
dbar
σradial
T + ∆T
T
Lugs
Forces transferred to bar at the lugs
∆x
T + ∆T
T
Lugs
Forces transferred to bar at the lugs
∆x
Axial cross-section of lug on reinforcement showing radial forces on grout surrounding the bar
dbar
σradial
Figure A.37 Free-body diagram of longitudinal bar with all load transferred
through lugs and pressure generated in the surrounding grout
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190
For design convenience the bond stress can be expressed as a function of
shear as shown in Equation (A.27). This relationship is valid in cases where the
bond between grout and reinforcement remains intact. Generally bond is broken
after the reinforcement yields, therefore this development does not apply to cases
where a plastic hinge may form. For practical reasons this analysis based on
Equation (A.27) is limited to out-of-plane loading. Since the resultant force
acting on the lugs acts at about 45 degrees, the radial stresses, σradial are also equal
to the bond stress, u, as shown in Equation (A.28).
barbarbar djdV
xdjdM
xdTu
πππ ⋅=
∆⋅⋅∆
=∆⋅
∆=
Equation (A.27)
barradial djd
Vuπ
σ⋅
== Equation (A.28)
These radial forces cause splitting tensile stresses along a section through
the wall at the center of the grouted core. Because the AAC has only about 15%
of the splitting tensile strength of the grout, its tensile strength is neglected. A
uniform distribution of splitting stresses across any section through the diameter
of the grout core is assumed as shown in Figure A.38a. Since the radial stresses
are symmetric about the centerline of the core (Figure A.38a), the net resultant of
those radial stresses perpendicular to the centerline is zero. The splitting tensile
stresses are resisted by the splitting tensile capacity of a section of grout, whose
area is the length of grout shown in Figure A.38b, multiplied by the length of a
section ∆x. The resistance to the splitting tensile stresses is expressed in Equation
(A.29). The resistance is increased by increasing the diameter of the core,
decreasing the diameter of the bar, or increasing the tensile strength of the grout.
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191
Length of grout supplying splitting resistance
dcore- dbar
2
dcore- dbar
2
Uniform splitting stresses across a section of grout
σradial
a) b)
Centerline of grouted cell
Length of grout supplying splitting resistance
dcore- dbar
2
dcore- dbar
2
Length of grout supplying splitting resistance
dcore- dbar
2
dcore- dbar
2
dcore- dbar
2
dcore- dbar
2
Uniform splitting stresses across a section of grout
σradial
a) b)
Centerline of grouted cell
Figure A.38 Stresses generated perpendicular to a cut along the diameter of a
grouted cell
xddfF barcoretceresis ∆−= )(tan Equation (A.29)
The uniform splitting stress across a section of grout as shown in Figure
A.38a is calculated by integration. Figure A.39a shows the radial stress acting at
the interface between the bar and grout. The vertical component of stress which
corresponds to a uniform splitting stress is calculated using geometry for a
differential section of the arc, ds (Figure A.39b). Integrating this expression for
the vertical component of force between angles of 0 and π yields the expression
for the total force generated by the splitting stress shown in Equation (A.30). If
the resultant of the uniform splitting tensile stress is set equal to the total force
supplied by the resistance of the grout (Figure A.38), Equation (A.31) is
generated. The splitting tensile strength, ft, is expressed in terms of the bond
stress in Equation (A.32).
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192
b)
ds
θσradial
c)
θ=0
ds=dbardθ
2
dbar2
θ=π
a)
σradial
Resultant from splitting stresses
b)
ds
θσradial
b)
ds
θσradial
c)
θ=0
ds=dbardθ
2
dbar2
θ=π
c)
θ=0
ds=dbardθ
2ds=dbardθ
2
dbar2
θ=π
a)
σradialσradial
Resultant from splitting stresses
Figure A.39 Calculation of force corresponding to the splitting tensile stresses
across a section of grout
∫∫ ∆=⋅∆=⋅∆=ππ
σθθσθσ00 2
sinsin xddd
xsdxF barradialbar
radialradialsplitting
Equation
(A.30)
xdxddf barradialbarcoret ∆=∆− σ)( Equation (A.31)
)()()(,barcorebar
bar
barcore
bar
barcore
barradialreqdt dddjd
Vddd
udddd
f−⋅⋅
=−
=−
=σ
Equation (A.32)
Based on this analysis, for reinforcement in the elastic stress range, the
acting splitting tensile stress can be calculated. In such a case the area ratio of
longitudinal steel may be increased beyond the proposed value of 3% for the
design provisions of Section A.2.8. These proposed design provisions permit area
ratios of longitudinal steel to grouted core up to 4.5%, provided that the splitting
tensile stress generated in the core (Equation (A.32)) is less than the available
splitting tensile strength. A detailed example of these calculations is presented in
a design example involving walls subject to out-of-plane loading. The proposed
design provisions in ACI 318-02 Code language are as follows:
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193
12.1.3 – The maximum ratio of vertical reinforcement to area of a grouted cell shall be 3%. It shall be permitted to use ratios of vertical reinforcement up to 4.5% if the reinforcement remains elastic throughout its entire length and the available splitting tensile strength of the grout is greater than the acting splitting tensile strength as defined by Equation (12-xx)
)( barcorebar
bart dddjd
Vdf
−⋅⋅= Equation (12-xx)
The splitting tensile strength of the grout shall be taken as '4 gf . If fg′ is not specified it shall be permitted to be taken as 2000 psi.
A.2.8 Analysis of the Maximum Permissible Area Ratio in a Plastic Hinge
Zone
If the reinforcement is located in a plastic hinge zone, compatibility of
strains no longer exists between the reinforcement and the surrounding grout, and
the splitting tensile stress cannot be determined using Equation (A.32). Based on
the cracking observed along the flexural reinforcement in the flexure-dominated
specimens (Section A.2.4), the proposed design provisions limit the area ratio to
3% in areas where a plastic hinge may form.
A.3 DESIGN EXAMPLES
A.3.1 Design of an AAC shear wall
Design the following two-story AAC shear wall. Material properties,
factored loads, and geometry are:
PAAC-5
psi 580 ' =AACf
fy = 60,000 psi (flexural reinforcement)
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194
Es = 29,000 Ksi
Factored axial load at each story, Pu = 35,000 lbs
Factored lateral load at each story, Fu = 18,000 lbs
Fu
Fu
7.5 ft
7.5 ft
20 ft
10 in.
24 in.
Pu
Pu
AAC wall
AAC wall
AAC flanges
AAC flanges
AAC wall
A.3.1.1 Flexural capacity
Determine factored bending moment at the base of the wall:
( ) ( ) ( ) . 0004,860, 12 )5.7( 000,18 12 15 18,000 inlbsM u −=+=
Determine flexural capacity at the base of the wall. Assume flexural
reinforcement at wall ends only, equal to 1 # 4 bar, located 24 in. from the wall
ends.
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195
10 in.
24 in.
24 in. 24 in. 96 in. 96 in.
24 in.
216 in.
1 # 4 bar 1 # 4 barAACflange AAC wall
AAC flange
Calculate forces in bars (T1 and T2) assuming that both bars are yielding:
T1 = T2 = As fy = 0.2 (60,000) = 12,000 lbs
For equilibrium:
C = Nu + T1 + T2
Nu = 2 (Pu) = 35,000 + 35,000 = 70,000 lbs
b a f 85.0C 'AAC=
. 6.5)2410( )580( 85.0)2( 000,12000,70
b 85.0 ' infCa
AAC
=+
+==
−
+
−
−=
2al
C 242l
T - 2l
216 TM ww2
w1n
lbsM n 000,020,112
6.5240 94,000 242
240 12,000- 2
240216 000,12 =
−
+
−
−=
( ) lbsM n 9,900,000 000,020,11 9.0 ==φ
φMn = 9,900,000 lbs-in. > Mu = 4,860,000 lbs-in. OK
Check if right bar (T2) is yielding.
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196
in. 8.4 0.675.6 a
1
===β
c
( ) ( ) 0.0086 0.003 8.424
4.824 AAC2 === εε
0.0021 29,000,000
60,000 Ef
s
yy ===ε
ε2 = 0.0086 > εy = 0.0021 OK
A.3.1.2 Shear capacity
Determine factored shear force and axial force at the base of the wall:
lbsFV uu 000,36)000,18( 2 2 ===
lbsu 000,70N =
Determine shear capacity at the base of the wall (web shear cracking):
wAAC
uAACwAAC
ltf
NfltV
4.2 1 9.0
'
' += φφ
( ) ( ) ( )( )( )
lbsVAAC 47,850 240 10 580 4.2
000,70 1 580 240 10 9.0 75.0 =+=φ
φVAAC = 47,850 lbs > Vu = 36,000 lbs OK
Determine factored shear force an axial force at 7.5 ft from the base of the
wall:
lbsFV uu 000,18 ==
lbsP uu 000,35N ==
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197
Determine shear capacity at 7.5 ft from the base of the wall (web shear
cracking):
( ) ( ) ( )( ) ( )
lbsVAAC 43,700 240 10 580 4.2
000,35 1 580 240 10 9.0 75.0 =+=φ
φVAAC = 43,700 lbs > Vu = 18,000 lbs OK
Determine shear capacity of bottom wall (crushing of the diagonal strut):
( )
4l 3
h
4l 3
h t wf 9.0 75.0 2
w2
w
strut'AAC
+
=AACVφ
in 60 4
240 4l
w wstrut ===
( ) ( ) ( ) ( )( )
( )lbs 93,960
4240 3 90
4240 3 90
60 10 580 9.0 75.0 22
=
+
=AACVφ
φVAAC = 93,960 lbs > Vu = 36,000 lbs OK
Determine sliding shear capacity of bottom wall and a thin-bed mortar
joint:
µ = 1 at a leveling bed joint
( )ussV N µφφ =
Neglect additional force in tensile steel:
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198
( ) ( )( ) lbsVss 500,52000,70 1 75.0 ==φ
φVss = 52,500 lbs > Vu = 36,000 lbs OK
µ = 0.75 at AAC to AAC joint
( )ussV N µφφ =
Neglect additional force in tensile steel.
( ) ( )( ) lbsVss 375,39000,70 75.0 75.0 ==φ
φVss = 39,375 lbs > Vu = 36,000 lbs OK
A.3.2 Design an AAC Shear Wall for Out-of-plane loads
PAAC-5
psi 580 ' =AACf
fy = 60,000 psi (flexural reinforcement)
Es = 29,000 ksi
Factored wind load on wall ρu = 110 lbs/ft2
Reinforcement in a 3 in. grouted cell at 4 ft. on center
h=10 ft
t=10 in.
Plan view of 4 ft. section of wall
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199
48 in.48 in.
Elevation of shear wall simply supported at top and bottom
A.3.2.1 Flexural capacity
Determine acting moment:
ftlbwu / 440 4ft lb/ft 110 width 2 =⋅=⋅= ρ
.000,66 5005, 8(10)440
8wl
22
inlbftlbM u −=−=⋅
==
Try #4 bar:
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200
lbfT y 000,12 60,0000.2 A s =⋅==
inbf
TaAAC
5.04858085.0
000,12'85.0
=⋅⋅
==
in -lb 57,000)2
0.5-(512 )2a-(dfA ys =⋅=⋅⋅=nM
φMn=0.9*57,000 lb-in=51,300 lb-in.<Mu Not Good
Try #5 bar:
lbfT y 600,18 60,0000.31 A s =⋅==
inbf
TaAAC
8.04858085.0
600,18'85.0
=⋅⋅
==
in -lb 5,7008)2
0.8-(518.6 )2a-(dfA ys =⋅=⋅⋅=nM
φMn=0.9*85,700 lb-in= 77,130 lb-in.>Mu O.K.
Check strain limits for this case:
c=a/β1=0.8/0.67=1.2
d=5
εs=0.003*(d-c)/c=0.0095>1.3εy=1.3*1.25*fy/Es=0.0033
Use a #5 bar
Asteel/Agrout=0.31/7.1=0.044=4.4%>3%
Perform an analysis to check the bond stress. In the case of out-of-plane
loads the reinforcement in the wall does not yield and no plastic hinge forms. In
this example, the classical bond stress analysis shown in the example can be used.
Check bond stress:
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201
Determine if reinforcement is yielding:
φMn=0.9*85,700 lb-in= 77,130 lb-in.>Mu=66,000 lb-in, reinforcement
will not be yielding. Since reinforcement will not be yielding consider case where
bond remains intact and express bond stress as a function of shear.
Determine shear and bond stress along the length of the wall. Based on
the bond stress determine the splitting tensile stress in the wall and compare to the
splitting tensile strength of the grout.
M (x)
Moment
V (x)
Shear
Mu=66,000 lbin
Vu= 2,200 lb
u (x)
Bond Stress
uu= 73.7 psi
M (x)
Moment
V (x)
Shear
Mu=66,000 lbin
Vu= 2,200 lb
u (x)
Bond Stress
uu= 73.7 psi
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202
lbsVu 22002
10440=
⋅=
psidarm
Vubar
u 280625.058.0
2200=
⋅⋅⋅=
⋅=
ππ
psidd
udf
barcore
bartreqd 7.73
)625.03(625.0280
)(=
−⋅
=−
=
psiff gtavailable 219300044 ===
The factored splitting tensile stress is less than the factored tensile strength
available. Use φ=0.75 which corresponds to shear.
uu = 74 psi < φft = 0.75(219)= 164 psi.
A.3.2.2 Shear capacity
Determine factored loads and maximum shear force for a single panel.
wu = 110 psf
( ) lbsLwV uu 100,1 2
10 110 2 2
2 ===
Determine shear capacity of floor panel:
lbsPAfV unAACAAC 520010245809.005.09.0 ' =⋅⋅=+=
φVAAC = 0.75*(5,200)= 3,900 lbs > Vu = 1,100 lbs OK
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203
APPENDIX B ACI 523.5R-xx Guide for using Autoclaved
Aerated Concrete Panels
B.1 INTRODUCTION
Appendix B consists of the first several draft chapters in a Guide for using
Autoclaved Aerated Concrete Panels, under development in ACI Committee
523A, Cellular Concrete. Much of the material in that draft chapter was
extensively rewritten for inclusion in the MS thesis of Argudo (2003). It is
presented here to give the reader basic background information on AAC.
B.1.1 Definition of Autoclaved Aerated Concrete
Autoclaved Aerated Concrete (AAC) is a low-density cementitious product of
calcium silicate hydrates in which the low density is obtained by the formation of
macroscopic air bubbles, mainly by chemical reactions within the mass during the
liquid or plastic phase. The air bubbles are uniformly distributed and are retained
in the matrix on setting, hardening, and subsequent curing with high-pressure
steam in an autoclave, to produce a cellular structure (Figure B.1). Material
specifications for this product are prescribed in ASTM C 1386.
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Figure B.1 Cellular structure of AAC
B.1.2 Typical Mechanical and Thermal Characteristics of AAC
In Table B.1, typical mechanical and thermal characteristics of AAC are
compared with those of conventional concrete, including conventional concrete
made with lightweight aggregates. AAC typically has one-sixth to one-third the
density of conventional concrete, and about the same ratio of compressive
strength, making it potentially suitable for cladding and infills, and for bearing-
wall components of low- to medium-rise structures. Its thermal conductivity is
one-sixth or less that of concrete, making it potentially energy-efficient. Its fire
rating is slightly longer than that of conventional concrete of the same thickness,
making it potentially useful in applications where fire resistance is important.
Because of its internal porosity, AAC has very low sound transmission, making it
potentially useful acoustically.
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Table B.1 Typical mechanical and thermal characteristics of AAC
Characteristic AAC Conventional
Concrete
density, pcf (kg/m3) 25 - 50 (400 - 800) 80 - 150 (1280 - 2400)
compressive strength, fc , psi
(MPa)
360 - 1090 (2.5 - 7.5) 1000 - 10000 (6.9 - 69)
thermal conductivity, Btu-
in/ft2-hr-F
0.75 - 1.20 6.0 - 10
fire rating, hours ≤ 8 ≤ 6
B.1.3 Historical Background of AAC
AAC was first produced commercially in Sweden, in 1923. Since that
time, its production and use have spread to more than 40 countries on all
continents, including North America, Central and South America, Europe, the
Middle East, the Far East, and Australia. This wide experience has produced
many case studies of use in different climates, and under different building codes.
In the US, modern uses of AAC began in 1990, for residential and
commercial projects in the southeastern states. US production of plain and
reinforced AAC started in 1995 in the southeast, and has since spread to other
parts of the country. A nationwide group of AAC manufacturers was formed in
1998 as the Autoclaved Aerated Concrete Products Association. This Guide is an
effort by the AAC technical community, including manufacturers, designers and
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researchers, to propose national design guidelines that could later be developed
into code provisions.
B.1.4 Applications of AAC Panels
AAC can be used to make unreinforced, masonry-type units, and also
factory-reinforced floor panels, roof panels, wall panels, lintels, beams, and other
special shapes (Figure B.2). These elements can be used in a variety of
applications including residential, commercial and industrial construction.
Reinforced wall panels can be used as cladding systems as well as load-bearing
and non-loadbearing exterior and interior wall systems. Reinforced floor and roof
panels can be efficiently used to provide the horizontal diaphragm system while
supporting the necessary gravity loads.
B.1.5 Scope and Objectives of this Guide
This Guide is limited to AAC with a density of 50 lb/ft3 (800 kg/m3) or
less. This Guide is written for structural designers. It addresses design using
factory-reinforced AAC elements. Design of AAC masonry is addressed in other
documents.
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Figure B.2 Examples of AAC structural elements
Design documents produced by ACI technical committees are classified as
standards or non-standards. The latter include “guides,” which are intended to
present directions for analysis, design, construction, materials, or testing on a
general basis. Their language is non-mandatory, permitting the user latitude in
judgment concerning particular needs.
The specific objectives of this Guide are:
a) To review the basic characteristics of AAC
b) To provide a capsule history of structural applications of AAC
c) To review the fabrication of AAC elements
d) To recommend structural design procedures for factory-reinforced AAC
elements
e) To recommend construction details for use with factory-reinforced AAC
elements
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The structural design procedures and construction details recommended
here are intended to result in AAC elements with adequate structural capacity,
durability, appearance and overall serviceability.
B.2 TYPICAL MATERIALS AND MANUFACTURE OF AAC
B.2.1 Materials Used in AAC
Materials for AAC vary with manufacture and location, and are specified
in ASTM C1386. They include some or all of the following:
a) Fine silica sand (ASTM C33, C144 or C332);
b) Class F fly ash (ASTM C618) with up to 12% loss on ignition (LOI);
c) Hydraulic cements (ASTM C150 or C595);
d) Calcined lime (ASTM C110);
e) Gypsum (ASTM C22);
f) Expansive agent, such as finely ground aluminum powder;
g) Mixing water (clean and free of deleterious substances); and
h) Reinforcement (ASTM A82), welded to form cages, with corrosion-
inhibiting coating.
B.2.2 Manufacture of AAC
Overall steps in the manufacture of AAC are shown in Figure B.3.
B.2.2.1 Preparation, Batching and Mixing of Raw Materials
Sand is ground to the required fineness in a ball mill, if necessary, and is
stored along with other raw materials. The raw materials are then batched by
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weight and delivered to the mixer. Measured amounts of water and expansive
agent are added to the mixer, and the cementitious slurry is mixed.
Figure B.3 Overall steps in manufacture of AAC
B.2.2.2 Casting, Expansion and Initial Hydration
Steel molds are prepared to receive the fresh AAC. If reinforced AAC
panels are to be produced, steel reinforcing cages are secured within the molds.
After mixing, the slurry is poured into the molds. The expansive agent creates
small, finely dispersed voids in the fresh mixture, which approximately triples in
volume in less than an hour in the molds.
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B.2.2.3 Cutting
Within a few hours after casting, the initial hydration of cementitious
compounds in the AAC gives it sufficient strength to hold its shape and support
its own weight. The material is removed from the molds (Figure B.4) and fed into
a cutting machine, which, using wires, sections the blocks and panels into the
required sizes and shapes (Figure B.5). After cutting, the units remain in their
original positions in the larger AAC block.
Figure B.4 Fresh AAC after removal of molds
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Figure B.5 Cutting AAC into desired shapes
B.2.2.4 Autoclaving
After cutting, the aerated concrete product is transported to a large
autoclave, where the curing process is completed (Figure B.6). Autoclaving is
required to achieve the desired structural properties and dimensional stability.
The process takes about 8 – 12 hours under a pressure of about 174 psi (12 Bars)
and a temperature of about 360 ºF (180 ºC) depending on the grade of material
produced. During autoclaving, the wire-cut units remain in their original
positions in the AAC block. After autoclaving, they are separated for packaging.
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Figure B.6 Autoclaving AAC
B.2.2.5 Packaging
AAC units are normally placed on pallets for shipping. Unreinforced units
are typically shrink-wrapped, while reinforced elements are banded only, using
corner guards to minimize potential localized damage that might be caused by the
banding.
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Figure B.7 Packaging of finished AAC units
B.2.2.6 AAC Strength Classes
AAC is produced in different densities and corresponding compressive
strengths, in accordance with ASTM C1386 (Precast Autoclaved Aerated
Concrete Wall Construction Units) and ASTM C 1452 (Standard Specification for
Reinforced Autoclaved Aerated Concrete Elements). Densities and
corresponding strengths are described in terms of “strength classes.” In each case,
the strength class corresponds to the specified compressive strength in MPa.
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Table B.2 Material characteristics of AAC in different strength classes
Strength
Class
Specified
Compressive
Strength
lb/in2 (MPa)
Average
Compressive
Strength
Nominal
Dry Bulk
Density
lb/ft3
(kg/m3)
Density Limits
lb/ft3 (kg/m3)
AAC 2.0 290 (2.0) 360 (2.5) 25 (400)
31 (500)
22 (350) - 28 (450)
28 (450) - 34 (550)
AAC 3.3 478 (3.3) 31 (500)
37 (600)
28 (450) - 34 (550)
34 (550) - 41 (650)
AAC 4.0 580 (4.0) 720 (5.0) 31 (500)
37 (600)
44 (700)
50 (800)
28 (450) - 34 (550)
34 (550) - 41 (650)
41 (650) - 47 (750)
47 (750) - 53 (850)
AAC 4.4 638 (4.4) 37 (600)
44 (700)
34 (550) - 41 (650)
41 (650) - 47 (750)
AAC 6.0 870 (6.0) 1090 (7.5) 44 (700)
50 (800)
41 (650) - 47 (750)
47 (750) - 53 (850)
B.2.3 Typical Dimensions of AAC Units
B.2.3.1 Plain AAC Wall Units
Typical dimensions for plain AAC wall units (masonry-type units) are
shown in Table B.3.
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Table B.3 Dimensions of plain AAC wall units
AAC Unit
Type
Width, in. (mm) Height, in. (mm) Length, in. (mm)
Standard Block 2 - 15 (50 - 375) 8 (200) 24 (610)
Jumbo Block 4 - 15 (100 - 375) 16 - 24 (400 - 610) 24 - 40 (610 - 1050)
B.2.3.2 Reinforced AAC Units
Dimensional tolerances, requirements for reinforcement, and other
requirements for reinforced AAC panels are specified in ASTM C1452, which
also cites C1386. Typical dimensions for reinforced AAC wall units (panels) are
shown in Table B.4.
Table B.4 Dimensions of reinforced AAC wall units
Product Type Thickness,
in. (mm)
Height or Width,
in. (mm)
Typical Length,
ft (mm)
Wall Panel 2 -15 (50 - 375) 24 (610) 20 (6090)
Floor Panel 4 -15 (100 - 375) 24 (610) 20 (6090)
Lintel / Beam 4 -15 (100 - 375) 8 - 24 (200 - 610) 20 (6090)
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B.2.4 Dimensional Tolerances
In accordance with ASTM C1386, dimensional tolerances for plain AAC
wall units are 1/8 in. (3 mm) in each dimension. Dimensional tolerances for
reinforced elements are given in ASTM C1452, and are listed in Table B.5.
Table B.5 Dimensional tolerances for reinforced AAC units
Dimension Floor or Roof Panels, in. (mm) Wall Panels, in.
(mm)
Length ± 0.20 (± 5) ± 0.20 (± 5)
Width ± 0.12 (± 3) ± 0.12 (± 3)
Thickness ± 0.12 (± 3) ± 0.12 (± 3)
Tongue ± 0.12 (± 3) ± 0.12 (± 3)
Groove ± 0.12 (± 3) ± 0.12 (± 3)
B.2.5 Identification and Marking of AAC Units
All reinforced AAC units should bear identifying symbol to include a
mark indicating the strength class, production identification code, and position
number for reinforced panels. Pallets of unreinforced AAC units should be
labeled with strength class, production identification code and size of units.
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B.3 STRUCTURAL DESIGN OF REINFORCED AAC ELEMENTS
B.3.1 Introductory Remarks regarding Design Provisions
This document is a guide. Its design provisions are non-mandatory, and
are a synthesis of design recommendations from the Autoclaved Aerated Concrete
Products Association, and from the results of research conducted at the University
of Alabama at Birmingham (UAB), the University of Texas at Austin (UT
Austin), and elsewhere.
In this chapter, the proposed design provisions are introduced in narrative
form. In Appendix C (Argudo 2003), more information is presented regarding
specific design provisions, and a commentary on those provisions.
The specific design provisions and their associated commentary of
Appendix C (Argudo 2003), are intended to be compatible in organization,
numbering and form with the design provisions of ACI 318, in order to facilitate
their use by concrete designers, and also to facilitate their future consideration, in
mandatory form, by ACI Committee 318. For that reason, the provisions are
arranged to refer directly to ACI 318-02. Additions and exceptions are
specifically noted. New subcategories are inserted for new design provisions.
Loads for structural design of AAC elements should be taken from
appropriate load codes, such as ASCE 7. Understrength factors (Φ-factors) for
AAC elements depend on the actions under consideration. They reflect the
statistical variability of the capacity, and the accuracy of the capacity-calculation
formulas. When failure is governed by yield and fracture of tensile
reinforcement, Φ-factors are justifiably identical to those used for reinforced
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concrete. When failure is governed by crushing or diagonal tension of the AAC
itself, Φ-factors are similar to those used for concrete. They may even be higher,
because the factory production of AAC leads to decreased variability in its
mechanical characteristics compared to conventional concrete.
The design provisions of this Guide are not intended for use with
unreinforced, masonry-type units. Design of those units is covered by provisions
currently under development within the Masonry Standards Joint Committee.
B.3.2 Proposed Design Provisions for Reinforced AAC Panels
B.3.2.1 Basic Design Assumptions
The proposed design provisions for reinforced AAC panels are based on
the same principles used for strength design of conventional reinforced concrete
elements: strain compatibility between AAC and reinforcement (with some
modifications as noted below); stress-strain behavior of AAC and reinforcement;
and equilibrium. The design strength of AAC in compression is based on a
specified design compressive strength, fAAC′. Compliance with that specified
compressive strength is verified by compressive strength testing, using ASTM
C1386, when the AAC panels are fabricated. The design strength of AAC in
tension is proposed as a function of the specified compressive strength. The
design strength of reinforcement in tension is proposed as the specified yield
strength.
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B.3.2.2 Combinations of Flexure and Axial Load
AAC panels are designed for combinations of flexural and axial load using
principles identical to those for conventional reinforcement. Nominal capacity is
computed assuming plane sections; tensile reinforcement is assumed to be
yielded; the stress in compressive reinforcement is computed based on its strain
and its stress-strain behavior; and the distribution of compressive stress in the
AAC is approximated by an equivalent rectangular stress block.
Because reinforced AAC panels usually have equal areas of tensile and
compressive reinforcement, flexural capacity is usually “tension-controlled” (in
the terminology of ACI 318-02. Sections are under-reinforced (in the
terminology of ACI 318-99).
B.3.2.3 Bond and Development of Reinforcement
Reinforcement in AAC panels consists of welded-wire mesh installed
when the panels are produced, and deformed reinforcement installed in 3- to 4- in.
grouted cores as the panels are erected.
Bond and development requirements for deformed reinforcement in grout
are identical to those used for concrete or masonry construction. Given the small
sizes of deformed bars used in AAC construction, bond between the grout and the
AAC itself does not govern the bond capacity.
Bond and development requirements for welded-wire fabric embedded in
AAC are quite different from those for conventional concrete, however. Because
the welded-wire fabric has a corrosion-resistant coating, bond strength between
the coated wire and the AAC itself is negligible. Bond strength comes from
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bearing of the cross wires against the AAC. For typical cross-wire spacings, local
crushing of the AAC under the cross wires can be assumed to redistribute the
bearing stresses under the cross wires, leading to a uniform bearing strength of
fAAC′ under every cross-wire. Multiplying this stress by the number of cross wires
and by the bearing area of each cross-wire gives the maximum force that can be
developed in the welded wire fabric (Figure B.8).
scross
sh
As Fs
faacdcrossfaacdcross
faacdcross faacdcross
scross
sh
As Fs
faacdcrossfaacdcross
faacdcross faacdcross
Figure B.8 Bond mechanism of welded-wire fabric in AAC
This maximum force in the welded-wire mesh can limit the flexural
capacity of a reinforced AAC panel.
B.3.2.4 Shear
As with conventional reinforced concrete elements, the shear resistance of
AAC elements is computed as the summation of a shear resistance due to the
AAC itself (VAAC), and a shear resistance due to reinforcement oriented parallel to
the direction of the shear.
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The shear resistance due to the AAC itself (VAAC) is computed using the
web-shear approach of ACI 318-02. The diagonal tension resistance of the AAC
is expressed in terms of its specified compressive strength, and principal tensile
stresses, including the effects of axial loads, are equated with this strength. This
produces an expression for VAAC in terms of the diagonal tension resistance of the
AAC, and the axial load on the element.
The shear resistance due to transverse reinforcement is computed based on
the cross-sectional area of the transverse reinforcement crossing a hypothetical
45-degree crack in the AAC. As explained in the previous subsection, it may also
be limited by bond and development of the reinforcement.
B.3.2.5 Bearing
To prevent local crushing of the AAC, nominal stresses in it are limited to
fAAC′. When AAC floor or roof panels bear on AAC walls, shear failure of the
edge of the wall is also possible. This is handled by limiting the shear stress on
potential inclined failure surfaces.
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B.4 HANDLING, ERECTION AND CONSTRUCTION WITH AAC UNITS
B.4.1 Handling of AAC Panels
AAC panels should be stored on suitably prepared supports, so that they
are prevented from warping. They should be carefully placed in their final
position without being overstressed or damaged. Instructions from the
manufacturer on how to handle the units should be followed. Special equipment
is usually used or recommended by the manufacturer to assist in the transportation
and erection of the units.
B.4.2 Erection of AAC Wall Panels
AAC panels are lifted and placed using specially designed clamps, and are
aligned using alignment bars.
B.4.2.1 Erection of AAC Cladding Systems
AAC panels can be used as non-load bearing cladding systems. This
application usually involves horizontally oriented panels attached to steel or
reinforced concrete frame. Erection of such panels follows these steps:
a) Ensure that supporting columns are plumb and true.
b) Set the bottom panel against the supporting columns and over the floor
slab or slab on ground, on top of a bed joint of conventional masonry
mortar. Make sure that the panel is true and level.
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c) Immediately after placing the first panel, fasten a wall anchor plate to the
column (using a dovetail or mechanically locking connector), and nail the
plate to the AAC panel. The back face of the panel should be flush with
the outer face of the column.
d) Place subsequent panels on top of the first one. The top and bottom faces
of the horizontal wall panels can have either a tongue and groove profile,
or a flat profile. Tongue and groove joints do not require mortar. Flat
joints are mortared with thin-bed mortar.
e) Seal horizontal and vertical joints with flexible sealant.
B.4.2.2 Erection of Vertical AAC Panels for Bearing-Wall Systems
Vertical AAC panels may also be used as a load-bearing wall system. In
such cases, the floor roof systems are usually designed and detailed as horizontal
diaphragms to transfer lateral loads to shear walls. The tops of the panels are
connected to the floor or roof diaphragms using a cast-in-place reinforced
concrete ring beam. This and many other structural details are addressed in the
next chapter.
When vertical wall panels are used in this way, they are set on a bedding
joint of conventional masonry mortar, with or without a waterproofing admixture.
Vertical wall panels are usually mortared together with thin-bed mortar.
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B.4.3 Erection of AAC Floor and Roof Panels
AAC floor and floor panels can be erected on concrete, steel or masonry
construction. All bearing surfaces should be level and minimum required bearing
areas (to prevent local crushing) should be maintained.
As in any precast construction system, care must be exercised in the installation of the
first panel to ensure correct alignment of the remaining panels. All floor and roof anchors should
be installed prior to placement of the panels, thus streamlining and expediting panel installation.
Most floor and roof panels are connected by keyed joints that are
reinforced and filled with grout to lock the panels together and provide diaphragm
action to resist lateral loads. A cast-in-place reinforced concrete ring beam is
normally placed along the perimeter of the diaphragm, completing the system.
B.4.4 Electrical and Plumbing Installations in AAC
Electrical and plumbing installations in AAC are placed in routed chases.
Care should be taken when laying out chases to ensure that the structural integrity
of the AAC elements is maintained. Do not cut reinforcing steel or reduce the
structural thickness of the AAC elements in critical areas. When analyzing the
AAC element is intended to span vertically, horizontal routing should be
permitted only in areas with low flexural and compressive stresses. In contrast,
when the AAC element is intended to span horizontally, vertical routing should be
minimized. When possible, it may be advantageous to provide designated chases
for large quantities of conduit or plumbing.
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B.4.5 Exterior Finishes for AAC
Unprotected exterior AAC deteriorates when exposed to cycles of freezing
and thawing while saturated. To prevent such freeze-thaw deterioration, and to
enhance the aesthetics and abrasion resistance of AAC, exterior finishes should be
used. They should be compatible with the underlying AAC in terms of thermal
expansion and modulus of elasticity, and should be vapor permeable. Many
different types of exterior finishes are available, and the most common are
discussed here.
B.4.5.1 Polymer-Modified Stuccos, Paints or Finish Systems
Polymer-modified stuccos, paints or finish systems are the most common
exterior finish for AAC. They increase the AAC’s water-penetration resistance
while allowing the passage of water vapor. Heavy acrylic-based paints containing
aggregates are also used to increase abrasion resistance. There is generally no
need to level the surface, and horizontal and vertical joints may be chamfered as
an architectural feature, or may be filled.
B.4.5.2 Masonry Veneer
Masonry veneer may be used over AAC panels in much the same way that
it is used over other materials. The veneer is attached to the AAC wall using
masonry ties. The space between the AAC and the masonry can be left open
(forming a drainage wall), or can be filled with mortar.
B.4.5.3 Finishes for Basement Walls
When AAC panels are used in contact with moist or saturated soil (for
example, in basement walls, the surface in contact with the soil should be coated
with a waterproof material or membrane. The interior surface should either
remain uncoated, or be coated with a vapor-permeable interior finish.
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B.4.6 Interior Finishes for AAC Panels
Interior finishes are used to enhance the aesthetics and durability of AAC.
They should be compatible with the underlying AAC in terms of thermal
expansion and modulus of elasticity, and should be vapor permeable. Many
different types of interior finishes are available, and the most common are
discussed here.
B.4.6.1 Interior Plasters
Interior AAC wall panels may have a thin coat of a mineral-based plaster
to achieve a smooth finished surface. Lightweight interior gypsum-based plaster
may provide a thicker coating to level and straighten walls, and to provide a base
for decorative interior paints or wall finishes. Interior plasters have bonding
agents to enhance their adhesion and flexibility, and are commonly installed by
either spraying or troweling.
B.4.6.2 Gypsum Board
When applied to the interior surface of exterior AAC walls, gypsum board
should be attached using pressure-treated furring strips. When applied to interior
walls, moisture-resistant gypsum board can be applied directly to the AAC
surface.
B.4.6.3 High-Durability Finishes for Commercial Applications
For commercial applications requiring high durability and low
maintenance, acrylic-based coatings are often used. Some contain aggregates to
enhance abrasion resistance.
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B.4.6.4 Ceramic Tile
When ceramic wall tile is to be applied over AAC, surface preparation is
normally necessary only when the AAC surface requires leveling. In such cases, a
Portland cement- or gypsum-based parge coat is applied to the AAC surface
before setting the ceramic tile. The ceramic tile should then be adhered to the
parged wall using either a cement-based thin-set mortar or an organic adhesive.
In moist areas such as showers, only a Portland cement-based parge coat should
be used, and the ceramic tile should be set with cement-based thin-set mortar
only.
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REFERENCES
1. Argudo 2003: Argudo, J., “Design Provisions for Reinforced AAC panels”,
M.S. thesis, Dept. of Civil Engineering, The University of Texas at Austin, August 2003.
2. ACI 318 2002: Building Code Requirements for Structural Concrete Code and Commentary, American Concrete Institute, Farmington Hills, MI.
3. ASTM C 476 (2002): Standard Specification for Grout for Masonry, American Society for Testing and Materials, West Conshohocken, PA, 2002.
4. ASTM C 1006 (2001): Standard Specification for Splitting Tensile Strength of Masonry Units, American Society for Testing and Materials, West Conshohocken, PA, 2001.
5. ASTM C 1386 (1998): Standard Specification for Precast Autoclaved Aerated Concrete (PAAC) Wall Construction Units, American Society for Testing and Materials, West Conshohocken, PA, 1998.
6. Drysdale, Hamid and Baker 1994: Drysdale, R. G., A. A. Hamid, L. R. Baker, Masonry Structures, Behavior and Design, Prentice-Hall, Englewood Cliffs, NJ, 1994.
7. Hsu and Mau 1992: Hsu, T. C., S. T. Mau, Concrete Shear in Earthquakes, Elsevier Applied Science, New York, NY, 1992.
8. Meyer 1998: Meyer C., Modelling and Analysis of Reinforced Concrete Structures for Dynamic Loading, Springer Wien, New York, NY, 1998.
9. Mo 1994: Mo, Y. L., Dynamic Behavior of Concrete Structures, Elsevier, New York, NY, 1994.
10. Park and Paulay 1975: Park R., T. Paulay, Reinforced Concrete Structures, John Wiley & Sons, New York, NY, 1975.
11. RILEM 1993: Autoclaved Aerated Concrete: Properties, Testing and Design, RILEM Recommended Practice, RILEM Technical Committees 78-MCA and 51-ALC, E & FN Spon, London.
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12. Tanner 2003: Tanner, J. E., “Design Provisions for Autoclaved Aerated Concrete (AAC) Structural Systems” Ph.D. dissertation, Dept. of Civil Engineering, The University of Texas at Austin, May 2003.
13. Varela 2003: Varela, J. L., “Proposed Values of R and Cd for AAC Structural Systems” Ph.D. dissertation, Dept. of Civil Engineering, The University of Texas at Austin, May 2003.
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VITA
Ulises Max Cancino was born on March 4, 1971 in Santiago, Chile. He earned
his Bachelors of Science in Engineering in 1996. During 1997 and 2002 he
worked as a structural engineer in different structural design offices in Santiago
and Temuco. This experience involved the design of reinforced concrete
buildings, malls, houses and factories. He became a Master’s degree candidate
at The University of Texas at Austin in 2002.
Permanent address: El Rosedal # 1983
Comuna: Santiago
Santiago, Chile
This thesis was typed by the author.